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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:03:01.95

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

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

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.37

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

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

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.87

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

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

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.27

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

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

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.79

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

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

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

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

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.35

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

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

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.86

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

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

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.13

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

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

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


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


-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:04:10.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


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

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


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

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


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

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


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

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.33
p-value of test                       :    0.92

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

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

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

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    1.95
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  119.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 4832.61
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


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

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.63

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


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

  j =  0                              :    1743165869958
  j =  1                              :        399908087
  j =  2                              :            45952
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


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

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

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


-----------------------------------------------
CPU time used                    :  00:02:31.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


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

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

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

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

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

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

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

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

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

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17197.98
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.10
p-value of test                       :    0.02


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.99
p-value of test                       :    0.94


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.08
p-value of test                       :    0.27


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

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.73
p-value of test                       :    0.94


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.05
p-value of test                       :    0.83


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:33.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.43
p-value of test                       :    0.09


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.92
p-value of test                       :    0.85


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.06
p-value of test                       :    0.78


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.33
p-value of test                       :    0.41


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.08
p-value of test                       :    0.73


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.95
p-value of test                       :    0.26


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.85
p-value of test                       :    0.12


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.65
p-value of test                       :    0.88


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.26
p-value of test                       :    0.09


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.34
p-value of test                       :    0.46


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.26
p-value of test                       :    0.60


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.18
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.90
p-value of test                       :    0.52


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.73
p-value of test                       :    0.75


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.97
p-value of test                       :    0.59


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.50
p-value of test                       :    0.83


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.28
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.18
p-value of test                       :    0.9991    *****


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

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



-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

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



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

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

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

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

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

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

-----------------------------------------------
CPU time used                    :  00:04:32.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

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

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.68
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.65
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000092752

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.30
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000033982

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

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

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:





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

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:46.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 0               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42860572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

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

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

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

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.75

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

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

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

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

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.78

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

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

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

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

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.30

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

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

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

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

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

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

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

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

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


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

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9903

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


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

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

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

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


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

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.46


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

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

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

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:48.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  125.32
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.68

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


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

  j =  0                              :    1743165869831
  j =  1                              :        399908341
  j =  2                              :            45825
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


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

  j =  0                              :    1743165869566
  j =  1                              :        399908872
  j =  2                              :            45558
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

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

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


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

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


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

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

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


-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

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

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


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

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.89
p-value of test                       :    0.88

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

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.34
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

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

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.41
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.29
p-value of test                       :    0.82


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.69
p-value of test                       :    0.81


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.30
p-value of test                       :    0.50


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.83
p-value of test                       :    0.52


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.75
p-value of test                       :    0.03


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.33
p-value of test                       :    0.83


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.40
p-value of test                       :    0.50


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.18
p-value of test                       :    0.41


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.23
p-value of test                       :    0.50


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.66
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.31
p-value of test                       :    0.78


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

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.58
p-value of test                       :    0.18


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

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.76
p-value of test                       :    0.60


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

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.64
p-value of test                       :    0.54


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

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.12
p-value of test                       :    0.67


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.33
p-value of test                       :    0.32


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.87
p-value of test                       :    0.70


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.64
p-value of test                       :    0.17


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.65
p-value of test                       :    0.95


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

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.16
p-value of test                       :    0.82


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

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.15
p-value of test                       :    0.54


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

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.94
p-value of test                       :    0.06


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

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:28.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

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

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.44e-3
p-value of test                       :    0.71

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

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

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

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

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

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:25.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.75
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.02
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999933668

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.73
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000147925

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.64
p-value of test                       :  7.5e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.29
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.63
p-value of test                       :    0.9957

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:





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

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:31.98

 All tests were passed




Server wird beendet - Lösche Semaphor 43909148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

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

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

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

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

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

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

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

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

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

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.71

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

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

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

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

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

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

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

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

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

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

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test

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


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

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

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

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5593
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4480
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


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

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

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

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


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

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

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

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


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

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

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

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:15.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


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

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

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

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

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

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          :  119
Value of the statistic                :  110.14
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.35
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

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

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

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


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

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.55

Generator state:




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

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

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

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


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

  j =  0                              :    1743165869870
  j =  1                              :        399908261
  j =  2                              :            45868
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

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

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


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

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:33.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


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

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

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

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


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

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

      Number of categories = 100000
      Expected number per category  = 100.00


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

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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

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



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.82
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

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

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

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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


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

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.37
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.46


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.99
p-value of test                       :    0.88


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.99
p-value of test                       :    0.75


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

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.15
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


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



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

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


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

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.87
p-value of test                       :    0.84


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

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.90
p-value of test                       :    0.75


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

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.02
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.71
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.72
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.51
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.25
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.82
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -2.68
p-value of test                       :    0.9963



-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.85
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.68
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.18
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:30.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.75
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999922577

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.45
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000034804

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:07.87

 All tests were passed




Server wird beendet - Lösche Semaphor 44597276.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:37.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.90
p-value of test                       :  9.8e-3

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.87
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.68
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.11
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45704
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869704
  j =  1                              :        399908596
  j =  2                              :            45696
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908411
  j =  2                              :            45787
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.50e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17619.06
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.87
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.00
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.67
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.99
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.08
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.72
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.35
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.44
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4689.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.33
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000052516

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999996704

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:30.67

 All tests were passed




Server wird beendet - Lösche Semaphor 45744156.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:51.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:11.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6953.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908264
  j =  2                              :            45862
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907899
  j =  2                              :            46046
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    : 2.52e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.32e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.72e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   11.01
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.44
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.34
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.42
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.68
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.21
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.83
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:33.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4298.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.45
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000114448

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.01
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000031618

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.61e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -2.11
p-value of test                       :    0.98

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:19.50

 All tests were passed




Server wird beendet - Lösche Semaphor 46727196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5283
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    6.21
p-value of test                       :  8.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.58
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.21
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908270
  j =  2                              :            45862
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907815
  j =  2                              :            46085
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.40
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.60
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.50
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.02
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.92
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.43
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.68
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.65
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.18
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:25.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999916016

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.82
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999863210

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.6e-3

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:23.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2S, t = 16        8.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47841308.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.13
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.50
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908186
  j =  2                              :            45907
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908378
  j =  2                              :            45802
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.62
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.81
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.49
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.61
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.80
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.32
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.05
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.61
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.54
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.77
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 9.94e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.58
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.34
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:22.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.41
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.18
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.20
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999920063

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.13
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000027214

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:52.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48758812.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.40
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  512.13
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1548.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908416
  j =  2                              :            45789
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908209
  j =  2                              :            45888
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.21
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17071.23
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.80
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.01
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.23
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.40
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.05
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.98
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.84
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11523.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.27
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000077482

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999993500

Normal statistic for number of bits   :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:42.25

 All tests were passed




Server wird beendet - Lösche Semaphor 49610780.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4517
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.90
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.89
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908614
  j =  2                              :            45681
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908445
  j =  2                              :            45773
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.22
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17586.63
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.71
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  574.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.74
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.66
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.32
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.77
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    2.65
p-value of test                       :  4.1e-3



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.54
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.64e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.28
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.02
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.78
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:32.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.36
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.30
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.18
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000185857

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.30
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000085234

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:52.51
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50626588.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.99
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.73
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.20
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908036
  j =  2                              :            45979
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908686
  j =  2                              :            45654
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.66
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.47
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17516.53
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.13
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.50
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.35
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.34
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.95
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.60
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  143.23
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.75
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    2.78
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.45
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:27.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.83
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000005686

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.60
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000065392

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:47.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51773468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.12
p-value of test                       :    0.9998    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9948

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.59
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908219
  j =  2                              :            45883
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908159
  j =  2                              :            45916
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.39e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17209.52
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   66.97
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.22
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.25
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  253.68
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:23.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3950.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.50
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999889994

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999920171

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52822044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:03.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.29
p-value of test                       :  6.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.45
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5297.99
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908316
  j =  2                              :            45836
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907925
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                1
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.64
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.54
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.02
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.39
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.04
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.30
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.69
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.70e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.63
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:04:22.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.65
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000038341

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.13
p-value of test                       :  3.6e-3


-----------------------------------------------
Total number of bits:  7999868391

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:22.79

 All tests were passed




Server wird beendet - Lösche Semaphor 53805084.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:14.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.34
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     558
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9931


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.46
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6873.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   82.52
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5212.50
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908975
  j =  2                              :            45505
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908295
  j =  2                              :            45851
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:10.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.72e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.25e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.18
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.35
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.36
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.80
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.35
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.75
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.11
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.03
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.73
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:36.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.75
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000011950

Normal statistic for number of bits   :   0.094
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.53
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000053650

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:41.62

 All tests were passed




Server wird beendet - Lösche Semaphor 54853660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.59
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5185.15
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46261
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870261
  j =  1                              :        399907483
  j =  2                              :            46251
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908361
  j =  2                              :            45809
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.88e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.72
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.80
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.81
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.76
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.38
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.89
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.26
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.34
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.41
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.19
p-value of test                       :    0.01

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.91
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.08
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:23.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5103.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000009640

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.90
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000033553

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    2.66
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:35.27

 All tests were passed




Server wird beendet - Lösche Semaphor 56033308.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:06.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7597
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:37.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.74
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.87
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46302
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870302
  j =  1                              :        399907403
  j =  2                              :            46288
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908537
  j =  2                              :            45727
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-5
p-value of test                       : 1 -  2.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17680.22
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.45
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.20
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.04
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.44
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.84
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.14
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:20.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.27
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:21.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.33
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000086392

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.20
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999952220

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57016348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     179
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.69
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.32
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46382
p-value of test                       :  9.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870382
  j =  1                              :        399907240
  j =  2                              :            46374
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45392
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869392
  j =  1                              :        399909221
  j =  2                              :            45382
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17712.66
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.38
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.61
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.18
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.26
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.18
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.24
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.15
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:21.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.12
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:20.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.98
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.70
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000071806

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.35
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000075868

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.67

 All tests were passed




Server wird beendet - Lösche Semaphor 57999388.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:13.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.83
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:47.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.28
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908348
  j =  2                              :            45826
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.85
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.12
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  4.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   89.79
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.97
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.31
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.35
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.16
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  601.98
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.75
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.44
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.46
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.02
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.78
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.09
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.41
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.76
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -7.25e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:34.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.40
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.26
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999977150

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.25
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999966284

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:16.62

 All tests were passed




Server wird beendet - Lösche Semaphor 58916892.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5318
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.72
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.94
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.87
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.30
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46281
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870281
  j =  1                              :        399907441
  j =  2                              :            46275
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45734
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869734
  j =  1                              :        399908539
  j =  2                              :            45720
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.66
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.31
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.57
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.72
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.94
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.73
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.46
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.31
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.74
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11562.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.66
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000099613

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.77
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000084421

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:35.37

 All tests were passed




Server wird beendet - Lösche Semaphor 60227612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1486
p-value of test                       :  6.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334606
  j =  1                              :        599997028
  j =  2                              :             1486
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1486
p-value of test                       :  6.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334606
  j =  1                              :        599997028
  j =  2                              :             1486
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9990    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.35
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.82
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.88
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.61
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46327
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870327
  j =  1                              :        399907351
  j =  2                              :            46317
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908199
  j =  2                              :            45899
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17200.55
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.38
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.66
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.47
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.27
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.02
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.20
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.81
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:25.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.16
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000109285

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.54
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999910925

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.58
p-value of test                       :  4.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.72
p-value of test                       :    0.9967

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:42.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            6.0e-4
 11  CollisionOver, t = 21           6.0e-4
 23  ClosePairs mNP1, t = 5          0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61210652.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    3.26
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.31
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.25
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.04
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:58.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45620
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869620
  j =  1                              :        399908763
  j =  2                              :            45614
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46196
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870196
  j =  1                              :        399907611
  j =  2                              :            46190
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    6.01
p-value of test                       :  9.9e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.71e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.70
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:41.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.19
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.95
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.48
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.20
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.64
p-value of test                       :  4.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.04
p-value of test                       :  1.2e-3

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.23
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.82
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.67
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:04:24.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.66
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000062758

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.10
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000123226

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:10.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                9.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62259228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:02.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.16
p-value of test                       :  7.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9911

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.59
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908602
  j =  2                              :            45693
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45483
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869483
  j =  1                              :        399909037
  j =  2                              :            45477
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.88e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.69e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:21.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.33
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.99
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.37
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.46
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.98
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.99
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.57
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.87
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.05
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:12.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.03
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.68
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:11.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:19.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.81
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.31
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999892850

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.98
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999984167

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:19:51.60

 All tests were passed




Server wird beendet - Lösche Semaphor 42893341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1260
p-value of test                       :    0.9977

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334380
  j =  1                              :        599997480
  j =  2                              :             1260
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:41.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.01
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908127
  j =  2                              :            45929
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907984
  j =  2                              :            46005
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.73
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.35
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.53
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.52
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.96
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.08
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.95
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.69
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999827396

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.02
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999960473

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:47.64

 All tests were passed




Server wird beendet - Lösche Semaphor 42991645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.32
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.30
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.56
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46164
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870164
  j =  1                              :        399907679
  j =  2                              :            46150
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908139
  j =  2                              :            45923
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.94e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.31e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.03
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.71
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17675.12
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.88
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.59
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.82
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.41
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.78
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.98
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.12
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.40
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.05
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:25.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.53
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000017431

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.56
p-value of test                       :  9.1e-3


-----------------------------------------------
Total number of bits:  8000135295

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:30.54

 All tests were passed




Server wird beendet - Lösche Semaphor 44040221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.42
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     817
p-value of test                       :    0.9973

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.30
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7394.98
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.05
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908872
  j =  2                              :            45558
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908840
  j =  2                              :            45574
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.40
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.32
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.24
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.33
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.67
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.78
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:42.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.06
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.58
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.81
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -2.28
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.51
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:21.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11588.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.50
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999993647

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.16
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000022354

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:50.61

 All tests were passed




Server wird beendet - Lösche Semaphor 45121565.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:10.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.81
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.86
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:55.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46320
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870320
  j =  1                              :        399907365
  j =  2                              :            46310
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908043
  j =  2                              :            45977
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.48e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.24
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  597.16
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.81
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.03
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.22
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.62
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.00
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.81
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.76
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.51
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.76
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:17.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:18.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.02
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:37.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.17
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.43
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000000379

Normal statistic for number of bits   : 3.00e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.37
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000044353

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:01.65

 All tests were passed




Server wird beendet - Lösche Semaphor 46137373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:10.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.80
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:33.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.22
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.22
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.35
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.68
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45500
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869500
  j =  1                              :        399909003
  j =  2                              :            45494
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908353
  j =  2                              :            45822
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.29e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.54
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17549.87
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.29
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.01
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.13
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.21
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.53
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.92
p-value of test                       :  2.0e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:31.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3949.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11610.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12048.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.98
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000062959

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.17
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000039568

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:46.12

 All tests were passed




Server wird beendet - Lösche Semaphor 47480861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:46.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.85
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.67
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908249
  j =  2                              :            45868
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.17
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.60
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.85
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.42
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.64
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.65
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.27
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.14
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.75
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10311.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:24.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3966.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.20
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999801770

Normal statistic for number of bits   :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.15
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000073087

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:50.52

 All tests were passed




Server wird beendet - Lösche Semaphor 48660509.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    3.69
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1553.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6822.97
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  150.79
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.53
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45408
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869408
  j =  1                              :        399909188
  j =  2                              :            45400
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907919
  j =  2                              :            46036
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.43e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  110.46
p-value of test                       :  6.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17727.02
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.45
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.03
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.01
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.49
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.64
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.11
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.44
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.56
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.50
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    6.31
p-value of test                       :  7.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.59
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.85e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :   10.58
p-value of test                       :  7.7e-6    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  120.42
p-value of test                       : 1 -  1.7e-6    *****

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.95
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.43
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999995456

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.22
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999943640

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:31.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           6.6e-4
 89  PeriodsInStrings, r = 20       1 -  1.7e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49545245.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7123
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     178
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:45.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.42
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.40
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.26
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.94
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46135
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870135
  j =  1                              :        399907733
  j =  2                              :            46129
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907670
  j =  2                              :            46165
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.03
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.73
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.15
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.16
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.72
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.99
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.72
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.39
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:19.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.49
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000131956

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.13
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000059587

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.67
p-value of test                       :  3.8e-3

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:49.12

 All tests were passed




Server wird beendet - Lösche Semaphor 50561053.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5558
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4546
p-value of test                       :  8.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:39.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.49
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.17
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.53
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.00
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907701
  j =  2                              :            46148
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908495
  j =  2                              :            45748
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.05
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.76
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.48
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.83
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.82
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.85
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.18
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.40
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.97
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9783.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:23.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.25
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000007309

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.19
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000044212

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:43.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         8.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51576861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7105
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9986

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.75
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:56.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908591
  j =  2                              :            45694
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907930
  j =  2                              :            46029
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.47e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.73
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.24
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.11
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.94
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.93
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.72
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.19
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.31
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.51
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.88
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.79
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.13
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.32
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:24.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.16
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.35
p-value of test                       :  2.2e-3


-----------------------------------------------
Total number of bits:  7999963566

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.39
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999950771

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.37

 All tests were passed




Server wird beendet - Lösche Semaphor 52592669.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.21
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.40
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7193.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.69
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908045
  j =  2                              :            45967
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46101
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870101
  j =  1                              :        399907803
  j =  2                              :            46091
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9913


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.75e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.89
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.70
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.57
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.27
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.98
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.57
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.77
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4794.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.72
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.09
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.98
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.95
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.46
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.81
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10335.10
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4673.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.83
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999968195

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   95.75
p-value of test                       :  4.0e-4    *****


-----------------------------------------------
Total number of bits:  7999784730

Normal statistic for number of bits   :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:18.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             4.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53641245.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5297
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:04.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9922

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    4.13
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.76
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.01
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908738
  j =  2                              :            45625
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908213
  j =  2                              :            45883
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.64e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.090
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.99
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.60
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.18
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.85
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.74
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.92
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.59
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    2.14
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.14e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.51
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10235.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:19.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.80
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999992840

Normal statistic for number of bits   :  -0.057
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999983174

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.20

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:46.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.73
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7246.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.05
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:55.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908845
  j =  2                              :            45573
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908223
  j =  2                              :            45881
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:20.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  3.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.83
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17177.56
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.87
p-value of test                       :    0.9928


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.28
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.53
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.46
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.86
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.68
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.27
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.03
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.63
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.87
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.37
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.38
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.74
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.82
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:29.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999987176

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.33
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999980801

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.49
p-value of test                       :  6.3e-3

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:24.53

 All tests were passed




Server wird beendet - Lösche Semaphor 55738397.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:09.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:12.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    3.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.96
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6822.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.65
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.89
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908621
  j =  2                              :            45679
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908308
  j =  2                              :            45840
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.01
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.40
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.60
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.50
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.95
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.32
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  458.58
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.60
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.45
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 4.97e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:42.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.02
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:31.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.66
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:42.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000023221

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.09
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999968582

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:40.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               3.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56786973.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7068
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:02:42.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.33
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.28
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908191
  j =  2                              :            45900
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908859
  j =  2                              :            45566
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.48
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.59
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.66
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.02
p-value of test                       :  8.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.11
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   45.02
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.33
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.55
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.77
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.80
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.98
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.24
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.52
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999966305

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.03
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000064651

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    4.51
p-value of test                       :  5.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.61
p-value of test                       :  4.5e-3

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:44.94

 All tests were passed




Server wird beendet - Lösche Semaphor 58064925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9952

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.95
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6870.06
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.63
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908330
  j =  2                              :            45826
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908217
  j =  2                              :            45890
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.48
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.09
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.67
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.32
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.79
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.29
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.79
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.53
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.52
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3932.74
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.31
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999830327

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999980573

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:55.10

 All tests were passed




Server wird beendet - Lösche Semaphor 59113501.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   29.10
p-value of test                       :  1.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.81
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.01
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.32
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907931
  j =  2                              :            46033
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45867
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869867
  j =  1                              :        399908270
  j =  2                              :            45859
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.41e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:40.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.34
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.04
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.09
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.48
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.80
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.82
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4767.08
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.56
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.14
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.17
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.37e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.16
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:22.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4638.03
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.29
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000016516

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.62
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999999584

Normal statistic for number of bits   : -3.29e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.16
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 26  SimpPoker, r = 0                1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60063773.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9918


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6836.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.47
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.69
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908146
  j =  2                              :            45921
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908399
  j =  2                              :            45793
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.57
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.11
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.06
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.56
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.08
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.57
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.30
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.11
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.09
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.76
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:20.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11574.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.49
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999857333

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000121420

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.32

 All tests were passed




Server wird beendet - Lösche Semaphor 61112349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.61
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.23
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908380
  j =  2                              :            45804
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907894
  j =  2                              :            46050
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.91
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.85
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.49
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.00
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.09
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.60
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.77
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.40
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:20.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.34
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -2.08
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.53
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000044407

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.44
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000005413

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :   0.096
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:35.14

 All tests were passed




Server wird beendet - Lösche Semaphor 62095389.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5543
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:58.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:03.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.27
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:10.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:33.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.80
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7355.29
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.70
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5228.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908894
  j =  2                              :            45553
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908173
  j =  2                              :            45909
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.47
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:56.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.13
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.66
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.38
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.75
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.34
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:34.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.15
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.64
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.7e-3

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.07
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.33
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:23.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.26
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999940067

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.82
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999844007

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:43.48

 All tests were passed




Server wird beendet - Lösche Semaphor 42926110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.17
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.23
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.21
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908017
  j =  2                              :            45987
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907813
  j =  2                              :            46092
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.71
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17811.34
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.60
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.07
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  597.44
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.56
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.40
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.70
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.96e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.58
p-value of test                       :    0.9913

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:25.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5055.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.71
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000126568

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.60
p-value of test                       :  2.1e-3


-----------------------------------------------
Total number of bits:  8000029179

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.36
p-value of test                       :  9.2e-3

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:57.05

 All tests were passed




Server wird beendet - Lösche Semaphor 43745310.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:45.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:12.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.89
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6813.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.70
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.71
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908180
  j =  2                              :            45901
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.12e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17144.45
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.83
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.09
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.37
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.85
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.43
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.16
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.54
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.29
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.81
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.95
p-value of test                       :    0.9984

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.63e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.25
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:10.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:30.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5044.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.23
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.40
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.69
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000019231

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.52
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999998135

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:11.03

 All tests were passed




Server wird beendet - Lösche Semaphor 44498974.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:46.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9910


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.94
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908092
  j =  2                              :            45948
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908081
  j =  2                              :            45958
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:33.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17601.16
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.84
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.26
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.79
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:25.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999833258

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.10
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999841874

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9917

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:12.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45350942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.34
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.35
p-value of test                       :  5.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     664
p-value of test                       :  5.3e-3

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9931


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.50
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.62
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.42
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.89
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.15
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46247
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870247
  j =  1                              :        399907510
  j =  2                              :            46239
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907871
  j =  2                              :            46060
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  8.9e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.07
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.27
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.43
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.78
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.55
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.97
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.33
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.91
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.00
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.43
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.25
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.99e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.32
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:25.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.66
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.16
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999843053

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.62
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999913853

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    2.49
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 52  SampleProd, t = 24             1 -  8.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46268446.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:08.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:12.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9930

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.89
p-value of test                       :  1.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6911.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4928.83
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907790
  j =  2                              :            46099
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.84
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.58
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.22
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.83
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.10
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.02
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.33
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.67e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:29.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:38.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4707.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.23
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:33.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.16
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000109177

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.79
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000092308

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:53.45

 All tests were passed




Server wird beendet - Lösche Semaphor 47251486.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4129
p-value of test                       :    0.9992    *****


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7532
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9995    *****

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:14.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.51
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4881.79
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:56.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907773
  j =  2                              :            46112
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:33.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.63e-6
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.22
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.65
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.75
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.61
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.94
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.07
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.19
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.37
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 3.36e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:33.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.24
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.91
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999879188

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.14
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999893237

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.63
p-value of test                       :    0.05

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:28.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 14  BirthdaySpacings, t = 3         0.9992 
 23  ClosePairs mNP, t = 5           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48529438.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5563
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4487
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.81
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.65
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.62
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:54.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45596
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869596
  j =  1                              :        399908814
  j =  2                              :            45584
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:02.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17372.52
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.89
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.91
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.03
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.16
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.32
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.48
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.42
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.23
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.66
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9910

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:21.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11547.53
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.47
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999966938

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000035248

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.95

 All tests were passed




Server wird beendet - Lösche Semaphor 49578014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.71
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:48.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908480
  j =  2                              :            45757
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907769
  j =  2                              :            46111
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:09.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.40
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   74.18
p-value of test                       :  8.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.54
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.69
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.81
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.64
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.03
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.39
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.79
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.72
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.77
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.29
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.69
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:31.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:39.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:33.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.23
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999957314

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.67
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999970898

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         : -8.92e-3
p-value of test                       :    0.50

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:01.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           8.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50593822.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.30
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.02
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908634
  j =  2                              :            45674
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.18
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.17
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.51
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.87
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.45
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5125.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.23
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.27
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.65
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4699.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.14
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000052273

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.02
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000071551

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.037
p-value of test                       :    0.49

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.76
p-value of test                       :  2.9e-3

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.85

 All tests were passed




Server wird beendet - Lösche Semaphor 51970078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5499
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:04.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.36
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4814.95
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908650
  j =  2                              :            45669
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.93e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17499.17
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.86
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.92
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.67
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.84
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.38
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.33
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.14
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.98
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9634.48
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:26.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.33
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999977459

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.16
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000111301

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.18
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.34

 All tests were passed




Server wird beendet - Lösche Semaphor 52985886.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.45
p-value of test                       :  1.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.26
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908659
  j =  2                              :            45666
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907904
  j =  2                              :            46042
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.87e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   66.94
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.90
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.40
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.34
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.01
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.86
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.26
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.44
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.16
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -2.64
p-value of test                       :    0.9958



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.43
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.28
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.80
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12011.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.89
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999966512

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.82
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999974489

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.13

 All tests were passed




Server wird beendet - Lösche Semaphor 54034462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9949

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    4.95
p-value of test                       :  3.0e-3

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.39
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:02.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6947.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.78
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.88
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908424
  j =  2                              :            45785
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908341
  j =  2                              :            45828
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.43e-6
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.26
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17589.69
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.57
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.40
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.75
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.42
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.22
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.81
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.70
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.26
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.23
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    2.96
p-value of test                       :  1.5e-3



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.53
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:27.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12127.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.03
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000135070

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.57
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000029641

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:24.54

 All tests were passed




Server wird beendet - Lösche Semaphor 54984734.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.76
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.85
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1330.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908062
  j =  2                              :            45966
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908157
  j =  2                              :            45920
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:30.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.95
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17589.30
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.71
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.00
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.13
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.74
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.14
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.87
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4728.63
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.77
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.86
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.04e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.35e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.06e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.76
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.47
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.86
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.57
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.44
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999928343

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.96
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999913853

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9938

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.07

 All tests were passed




Server wird beendet - Lösche Semaphor 56000542.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5260
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4181
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.87
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1298.67
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.21
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.54
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.56
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:57.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908599
  j =  2                              :            45693
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908136
  j =  2                              :            45929
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.57e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.18
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.91
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.99
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.76
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.11
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.01
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.91
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.17
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -2.06
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.85e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.78
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.31
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:21.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5041.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.95
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000107086

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.27
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000104611

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.40
p-value of test                       :    0.9918

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:29.12

 All tests were passed




Server wird beendet - Lösche Semaphor 57049118.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.99
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    2.62
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1555.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.68
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.63
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908635
  j =  2                              :            45681
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907788
  j =  2                              :            46094
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:04:59.35

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


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CPU time used                    :  00:02:30.64

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


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CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


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CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


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CPU time used                    :  00:02:02.35

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

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CPU time used                    :  00:01:56.39

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

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CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

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CPU time used                    :  00:01:36.61

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.42e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

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CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

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CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
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   N =  1,  n = 2000000000,  r =  0,   k = 1


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Normal statistic                      :    1.93
p-value of test                       :    0.03

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CPU time used                    :  00:00:23.71

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


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Normal statistic                      :    1.54
p-value of test                       :    0.06

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CPU time used                    :  00:00:23.69

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

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CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

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CPU time used                    :  00:01:43.19

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   67.73
p-value of test                       :    0.45

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CPU time used                    :  00:00:50.23

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   82.10
p-value of test                       :    0.10

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CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

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CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   26.29
p-value of test                       :    0.91

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CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.76
p-value of test                       :    0.89

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CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   30.18
p-value of test                       :    0.78

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CPU time used                    :  00:00:56.30

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
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   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   20.44
p-value of test                       :    0.88

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CPU time used                    :  00:01:45.89

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.69
p-value of test                       :    0.9971

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CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.39
p-value of test                       :    0.08

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CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


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Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

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CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

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CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

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CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

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CPU time used                    :  00:01:08.19

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.22
p-value of test                       :    0.67

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CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.61
p-value of test                       :    0.27



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CPU time used                    :  00:00:53.23

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.08
p-value of test                       :    0.99


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Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.91
p-value of test                       :    0.62


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.27
p-value of test                       :    0.10


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.78
p-value of test                       :    0.76


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.59
p-value of test                       :    0.10


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CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.02
p-value of test                       :    0.75


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.21
p-value of test                       :    0.79


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.50
p-value of test                       :    0.06


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


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CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.89
p-value of test                       :    0.25


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Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.46
p-value of test                       :    0.62


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.42
p-value of test                       :    0.46


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CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.32
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.76
p-value of test                       :    0.15


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.69
p-value of test                       :    0.25


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CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.37
p-value of test                       :    0.14


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.59
p-value of test                       :    0.42


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.51
p-value of test                       :    0.38


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.08
p-value of test                       :    0.77


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CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.21
p-value of test                       :    0.02


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4789.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.73
p-value of test                       :    0.61


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.84
p-value of test                       :    0.45


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CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



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CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



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CPU time used                    :  00:02:21.77

Generator state:




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HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.05
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.33
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:23.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.00
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999893048

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.22
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000002815

Normal statistic for number of bits   :   0.022
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.09

 All tests were passed




Server wird beendet - Lösche Semaphor 57933854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.17
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.63
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908359
  j =  2                              :            45816
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908133
  j =  2                              :            45923
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.71e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.11e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.75
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17715.60
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.74
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.59
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  425.62
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.42
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.81
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4813.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.94
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.71
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.95
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.44
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:19.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.30
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999945347

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.49
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000106693

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:02.97

 All tests were passed




Server wird beendet - Lösche Semaphor 58884126.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:47.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:05.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.61
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  285.02
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7175.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:28.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908306
  j =  2                              :            45841
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908106
  j =  2                              :            45944
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:31.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.12e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.43
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.29
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.24
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.13
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.33
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.52
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4801.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.08
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.44
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:19.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.63
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999962627

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.52
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999913382

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:13.54

 All tests were passed




Server wird beendet - Lösche Semaphor 59932702.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:06.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.71
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.50
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5129.07
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908360
  j =  2                              :            45817
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908037
  j =  2                              :            45974
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:37.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.43
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.43
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.48
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.44
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.58
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.17
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9763.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -3.51e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:19.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.86e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4680.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.78
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999895826

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.84
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999940967

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.70
p-value of test                       :  3.5e-3

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:01.90

 All tests were passed




Server wird beendet - Lösche Semaphor 60948510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:47.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6880.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.82
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.85
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.07
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:53.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908757
  j =  2                              :            45614
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908144
  j =  2                              :            45919
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.44e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.63
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.35
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.10
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  121.33
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.66
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.29
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.99
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.38
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.14
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.32
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.39
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:19.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.19
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4316.95
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999907889

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.22
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000002371

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:59.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 C (L=1000, r=0)     4.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61964318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:44.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:58.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1364.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.71
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4920.20
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46117
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870117
  j =  1                              :        399907768
  j =  2                              :            46113
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908111
  j =  2                              :            45940
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.17
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:33.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.73
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.34
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.29
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.16
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.30
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.72
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.42
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.13
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.16
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.33
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:16.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.56
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.78e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:22.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11670.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12160.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.36
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999954983

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.65
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999887771

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.9908

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:49.73

 All tests were passed




Server wird beendet - Lösche Semaphor 42958879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:44.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.91
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4885.34
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908736
  j =  2                              :            45626
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908381
  j =  2                              :            45805
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.97
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.12
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.95
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  472.09
p-value of test                       :  6.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.27
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.46
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10291.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:26.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4758.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.28
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999941129

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.67
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000113371

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:13.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   6.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43188255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:37.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.64
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:10.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908570
  j =  2                              :            45712
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907571
  j =  2                              :            46210
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   35.99
p-value of test                       :    0.9993    *****

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.05
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17699.58
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.06
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.59
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.63
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.60
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.57
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.81
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.37
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.65
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:21.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.88
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:27.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.56
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.79
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000092167

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.50
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999969284

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:21.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44236831.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5547
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:45.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.13
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.68
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.79
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45819
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869819
  j =  1                              :        399908367
  j =  2                              :            45809
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907780
  j =  2                              :            46104
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    5.26
p-value of test                       :  2.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.66
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17631.91
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.59
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.62
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.51
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.62
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.38
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.66
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.58
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.10
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.33
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:25.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5084.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11945.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.31
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000072937

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.27
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000007555

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:07.43

 All tests were passed




Server wird beendet - Lösche Semaphor 45219871.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:41.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6941.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.77
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.01
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:36.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908140
  j =  2                              :            45921
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907753
  j =  2                              :            46122
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.95e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.93
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.19
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.65
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.88
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.82
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.62
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.38
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.05
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:35.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4634.47
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.55
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000133246

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.88
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999918278

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:50.72

 All tests were passed




Server wird beendet - Lösche Semaphor 46235679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5296
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7516
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:37.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.68
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.05
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907986
  j =  2                              :            46001
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908460
  j =  2                              :            45761
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   52.50
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17524.15
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.69
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.54
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5213.01
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.60
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.59
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.35e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.63
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.43
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10296.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:27.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4384.01
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.52
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000112048

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.74
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000069964

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:06.70

 All tests were passed




Server wird beendet - Lösche Semaphor 47382559.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5542
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7233.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.44
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5157.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908289
  j =  2                              :            45848
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.81e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.71e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.39e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.98
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.18
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.53
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.73
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.37
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.24
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.91
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.17
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.07
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.64
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.16
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.46
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.69
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.13
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.67
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.52
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.36
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:32.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.26
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.56
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000068926

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.42
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999815624

Normal statistic for number of bits   :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:58.78

 All tests were passed




Server wird beendet - Lösche Semaphor 48365599.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5292
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.15
p-value of test                       :  2.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.23
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  174.28
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:15.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.63
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:21.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908499
  j =  2                              :            45746
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908044
  j =  2                              :            45969
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 4.27e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.22e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.59
p-value of test                       :  3.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17019.66
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   63.65
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.68
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.67
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.40
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.48
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.59
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.35
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.66
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.95
p-value of test                       :    0.9959


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.22
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.39
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:42.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:31.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 3.13e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:37.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.48
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000239614

Normal statistic for number of bits   :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.20
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000023350

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:20.79

 All tests were passed




Server wird beendet - Lösche Semaphor 49938463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:07.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.12
p-value of test                       :  9.7e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.82
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.15
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:29.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.38
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908554
  j =  2                              :            45720
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908613
  j =  2                              :            45689
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:20.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.43
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.77
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.01
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.94
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.16
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.47
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.33
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.92
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.32
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.00
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:22.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.49
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000077695

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.36
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999999338

Normal statistic for number of bits   : -5.23e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.27e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:51.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           9.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51052575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.89
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908345
  j =  2                              :            45823
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908554
  j =  2                              :            45720
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.92
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.10
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.75
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.70
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.20
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.19
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.45
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.10
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.48
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.87
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.95
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.38
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999930842

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.94
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000080809

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.55
p-value of test                       :    0.9946

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:27.37

 All tests were passed




Server wird beendet - Lösche Semaphor 52101151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9980

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   82.30
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908366
  j =  2                              :            45814
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908663
  j =  2                              :            45661
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17691.98
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.89
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.18
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.68
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.84
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.49
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.26
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.97
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.42
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.14
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:28.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.57
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.43
p-value of test                       :    0.9925



-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.31e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.90
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.53
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:20.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.57
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000227428

Normal statistic for number of bits   :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.66
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000045307

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:03.07

 All tests were passed




Server wird beendet - Lösche Semaphor 53149727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7520
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:44.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1301.63
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.64
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45480
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869480
  j =  1                              :        399909042
  j =  2                              :            45476
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908310
  j =  2                              :            45836
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.90e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.59e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.71
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.91
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  168.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.49
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.22
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.79
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.50
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  301.19
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.09
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.62
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.83
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000043957

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.99
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999989279

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:01.50
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54165535.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.32
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:07.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.94
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.54
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908629
  j =  2                              :            45681
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46394
p-value of test                       :  8.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870394
  j =  1                              :        399907213
  j =  2                              :            46392
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  106.31
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    6.41
p-value of test                       :  6.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  188.84
p-value of test                       :  5.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17210.50
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.54
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.65
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.52
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.48
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.23
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.45
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.79
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.90
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.25
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  149.15
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:17.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12089.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.91
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000066493

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999961004

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.83e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:02.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          5.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55181343.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4185
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.02
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.21
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45681
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869681
  j =  1                              :        399908642
  j =  2                              :            45673
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907944
  j =  2                              :            46016
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.28e-5
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.76e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.064
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.81
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17054.75
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.20
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.00
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.28
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.74
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.31
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.10
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.55
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.76
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9719.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:20.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3989.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12147.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.54
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999892583

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.58
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000178540

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.74
p-value of test                       :    0.9969

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:53.26

 All tests were passed




Server wird beendet - Lösche Semaphor 56164383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:05.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  509.71
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7012.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.29
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:59.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908755
  j =  2                              :            45618
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45594
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869594
  j =  1                              :        399908814
  j =  2                              :            45590
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.00
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.70
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.25
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.87
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.96
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.82
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.76
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.49
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.52
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.95
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000042601

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.73
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000031795

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.02

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.64

 All tests were passed




Server wird beendet - Lösche Semaphor 57212959.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5207
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7061
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  509.85
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.35
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   37.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.73
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908346
  j =  2                              :            45821
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907592
  j =  2                              :            46195
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17729.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.56
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.47
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.78
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.23
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.17
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.88
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.51
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.81
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.78
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.50
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999997421

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.80
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000004045

Normal statistic for number of bits   :   0.032
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:46.15

 All tests were passed




Server wird beendet - Lösche Semaphor 58195999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.92
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.02
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46173
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870173
  j =  1                              :        399907657
  j =  2                              :            46167
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907862
  j =  2                              :            46063
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.27
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.13
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.43
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.16
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.31
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.34
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.66e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.76
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:18.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.62
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999889946

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.26
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000020152

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:34.17

 All tests were passed




Server wird beendet - Lösche Semaphor 59408415.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:40.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.35
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.16
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907892
  j =  2                              :            46048
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908682
  j =  2                              :            45650
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.50

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.19
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.59
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.36
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.92
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.29
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.10
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.49
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.97
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.77
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9651.83
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:18.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4323.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.02
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000119776

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.24
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000130435

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:37.72

 All tests were passed




Server wird beendet - Lösche Semaphor 60391455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4478
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:03.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.83
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.66
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908265
  j =  2                              :            45860
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908482
  j =  2                              :            45756
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17578.44
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.73
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.97
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.80
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.04
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.38
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.67
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.61
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    2.03
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.36
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.95e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:09.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4271.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.69
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000067519

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.63
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000006517

Normal statistic for number of bits   :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:29.78

 All tests were passed




Server wird beendet - Lösche Semaphor 61374495.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.75
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.33
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908532
  j =  2                              :            45731
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908229
  j =  2                              :            45875
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.78
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.37
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.83
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.07
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.31
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.95
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.94
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.50
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.67
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.88
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.33
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.92
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.70e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.93
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9727.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:10.63

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.31
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000037087

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.19
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999924653

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    2.66
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n93, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:38.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62390303.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.61
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908222
  j =  2                              :            45883
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908100
  j =  2                              :            45947
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.83
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.16
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.74
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.09
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.98
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.85
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.80
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.60
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.36
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999963188

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.23
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000115771

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:49.68

 All tests were passed




Server wird beendet - Lösche Semaphor 41975809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:17.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.98
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.61
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.41
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.00
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.75
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:58.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908215
  j =  2                              :            45885
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908577
  j =  2                              :            45704
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.61e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.94
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.84
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.43
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.31
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.30
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.37
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  300.12
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.09
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.23
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.81
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.78
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9918.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.90
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.97
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:33.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.62
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000033625

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.56
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000046297

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.70e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:18.67

 All tests were passed




Server wird beendet - Lösche Semaphor 43876353.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7088
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:16.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.45
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   19.78
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.54
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:57.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46320
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870320
  j =  1                              :        399907365
  j =  2                              :            46310
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907796
  j =  2                              :            46096
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.39
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 6.03e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.60
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17116.27
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.05
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.20
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.47
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.77
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.86
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.50
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.23
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.58e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.77e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.12
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.70
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.86
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5178.34
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.28
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.94
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999940694

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000029536

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:35.95

 All tests were passed




Server wird beendet - Lösche Semaphor 44793857.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4511
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7096
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:02:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.17
p-value of test                       :  7.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     643
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.47
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.76
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.74
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46239
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870239
  j =  1                              :        399907524
  j =  2                              :            46235
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46049
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870049
  j =  1                              :        399907905
  j =  2                              :            46043
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17069.79
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.14
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.13
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.59
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.53
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.27
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.95
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.04
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11522.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.82
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999928400

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.59
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000058387

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:34.44

 All tests were passed




Server wird beendet - Lösche Semaphor 45678593.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1333.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.77
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.76
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46329
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870329
  j =  1                              :        399907343
  j =  2                              :            46327
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:30.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.09e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.80
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.39
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.83
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.04
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.89
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.84
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.97
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.70
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.76
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.01
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.05
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.05
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.23
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.80
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.33
p-value of test                       :    0.01

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11369.64
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.50
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000070663

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.21
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999924497

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:43.03

 All tests were passed




Server wird beendet - Lösche Semaphor 46596097.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9910

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  487.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7215.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.41
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.19
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908257
  j =  2                              :            45867
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17646.46
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.34
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.65
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.09
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.27
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.22
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.38
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.49
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.25
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.56
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.90
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.34
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -2.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.05
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.60
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000050440

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.75
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000072535

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    : 2.09e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9939

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:26.93

 All tests were passed




Server wird beendet - Lösche Semaphor 47546369.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     828
p-value of test                       :    0.9920

Stat. AD (mNP2)                       :    4.16
p-value of test                       :  7.3e-3

Stat. AD after spacings (mNP2-S)      :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:12.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.54
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7232.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.09
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.24
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:59.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908040
  j =  2                              :            45980
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908716
  j =  2                              :            45636
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.69e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.28e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.22
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.40
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.93
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.35
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.97
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.55
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.43
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.61
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.25
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.69
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.66
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    2.17
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.38
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.18
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:10.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999841034

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.71
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000100234

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.57

 All tests were passed




Server wird beendet - Lösche Semaphor 48562177.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.02
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:05.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4943.05
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:56.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908782
  j =  2                              :            45603
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908302
  j =  2                              :            45843
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.84
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.42
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.01
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.13
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.43
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.01
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.08
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.21
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.46
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.50
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4946.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000099319

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.09
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999961295

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.95

 All tests were passed




Server wird beendet - Lösche Semaphor 49545217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.88
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.20
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7225.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:06.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.93
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908530
  j =  2                              :            45729
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908143
  j =  2                              :            45927
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17155.75
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.13
p-value of test                       :  8.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.95
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.23
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.94
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9657.03
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:11.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11569.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.41
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999881327

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.99
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000071920

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:28.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50495489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  287.26
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:06.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.82
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.19
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908215
  j =  2                              :            45888
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908840
  j =  2                              :            45574
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.17
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9966


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17580.04
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.14
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.61
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.47
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.51
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.42
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.49
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.39
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.27
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.05
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.83
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.80
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-3
p-value of test                       :    0.9917

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10341.72
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.99
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11505.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.14
p-value of test                       :    0.9977


-----------------------------------------------
Total number of bits:  8000035731

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.31
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999936632

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:31.20

 All tests were passed




Server wird beendet - Lösche Semaphor 51544065.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  296.01
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:54.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46321
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870321
  j =  1                              :        399907360
  j =  2                              :            46317
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907963
  j =  2                              :            46011
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.89
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.91
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.20
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.58
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.70
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.44
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.02
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.09
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.25
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.79
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.18
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.60
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.27
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9725.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.13
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000102310

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.28
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999954311

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :   0.099
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:56.19

 All tests were passed




Server wird beendet - Lösche Semaphor 52559873.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9936


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    3.89
p-value of test                       :  9.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.45
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.01
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.37
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.23
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.94
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.48
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:56.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46019
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870019
  j =  1                              :        399907964
  j =  2                              :            46015
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908505
  j =  2                              :            45737
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.31
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.06
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.47
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.29
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.88
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.61
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -2.05
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.60
p-value of test                       :    0.9997    *****

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.78
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4253.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.26
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.55
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999989078

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.91
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000094012

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 86  LongestHeadRun, r = 0           0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53608449.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9918

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:19.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.55
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:20.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7158.40
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.36
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46133
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870133
  j =  1                              :        399907738
  j =  2                              :            46125
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907887
  j =  2                              :            46052
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17283.61
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.56
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.72
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.66
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.28
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.73
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.05
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.63
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.09
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.06
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.93
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.29
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.63
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.67
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.16e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11599.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.94
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999864797

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.75
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000070885

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.11
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:14.03

 All tests were passed




Server wird beendet - Lösche Semaphor 54657025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4525
p-value of test                       :  2.3e-3


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9967


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.17
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.61
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.13
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907749
  j =  2                              :            46115
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908409
  j =  2                              :            45794
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.43e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17175.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.00
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.76
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.50
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.09
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.87
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.86
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.35
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.56
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.03
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9716.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.08
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000133891

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.24
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000086152

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.57

 All tests were passed




Server wird beendet - Lösche Semaphor 55672833.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.44
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.03
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.80
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908151
  j =  2                              :            45917
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908560
  j =  2                              :            45711
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.47
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.66
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.38
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:40.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.91
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.00
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.07
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  416.28
p-value of test                       :    0.9974


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.98
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.81
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.39
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.61
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.62
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12040.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.87
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000060373

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.72
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999923432

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    2.88
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:28.72

 All tests were passed




Server wird beendet - Lösche Semaphor 56688641.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5238
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9952

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.52
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.13
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908057
  j =  2                              :            45964
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908436
  j =  2                              :            45770
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.67e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.023
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.10
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.07
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.41
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  315.11
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.30
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.08
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.23
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.81e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.06
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.65
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.06
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000108463

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.86
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999974123

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.067
p-value of test                       :    0.47

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:05.07

 All tests were passed




Server wird beendet - Lösche Semaphor 57737217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.29
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.00
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.15
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45649
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869649
  j =  1                              :        399908705
  j =  2                              :            45643
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907541
  j =  2                              :            46225
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.50
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17203.95
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.28
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.51
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.23
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.92
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.73
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4749.85
p-value of test                       :    0.9944


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.12
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.78
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.27
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10113.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.74
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999788615

Normal statistic for number of bits   :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.80
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000000541

Normal statistic for number of bits   : 4.28e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:00.75

 All tests were passed




Server wird beendet - Lösche Semaphor 58785793.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.83
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.05
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.87
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.55
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.98
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46273
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870273
  j =  1                              :        399907459
  j =  2                              :            46263
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908507
  j =  2                              :            45742
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:02:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17384.29
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.73
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.47
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.55
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.58
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.84
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.32
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.80
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.64
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.52
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10336.10
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5061.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.03
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999813380

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999881939

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.030
p-value of test                       :    0.51

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:42.73

 All tests were passed




Server wird beendet - Lösche Semaphor 59899905.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5572
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9997    *****

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.39
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:05.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.74
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5239.16
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908376
  j =  2                              :            45809
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907977
  j =  2                              :            46004
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.8e-3


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.83
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.89
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.53
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  172.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.00
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.44
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.12e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.29
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.68
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.24
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999936389

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.39
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999971615

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:54.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60981249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7556
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:47.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.64
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908789
  j =  2                              :            45601
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46179
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870179
  j =  1                              :        399907644
  j =  2                              :            46175
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.74
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.02
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.67
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.82
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.33
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.28
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.06
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.81
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.04
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9724.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.76
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000064897

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.08
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999896861

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         : 2.80e-3
p-value of test                       :    0.50

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:46.86

 All tests were passed




Server wird beendet - Lösche Semaphor 61997057.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.44
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    3.57
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     342
p-value of test                       :  9.3e-3

Stat. AD (mNP2)                       :    3.57
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:24.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.75
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5020.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46369
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870369
  j =  1                              :        399907265
  j =  2                              :            46363
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908183
  j =  2                              :            45901
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17098.47
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.71
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.62
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.53
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.85
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.20
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.19
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.57
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.00
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4389.79
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.13
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000008659

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.57
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000098278

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:23:22.37

 All tests were passed




Server wird beendet - Lösche Semaphor 42008578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1477
p-value of test                       :  1.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334597
  j =  1                              :        599997046
  j =  2                              :             1477
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:40.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4479
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9958


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.39
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7014.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.57
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.51
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.90
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908822
  j =  2                              :            45583
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46264
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870264
  j =  1                              :        399907473
  j =  2                              :            46262
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.74e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.99
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17268.92
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.25
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.91
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.42
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.41
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.41
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.25
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.32
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.31
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.36
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:32.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5116.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000002515

Normal statistic for number of bits   :   0.020
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.47
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000029788

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:08.35

 All tests were passed




Server wird beendet - Lösche Semaphor 43712514.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.54
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.55
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46144
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870144
  j =  1                              :        399907718
  j =  2                              :            46132
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908271
  j =  2                              :            45860
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.95
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.42
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.51
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.94
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  199.40
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.59
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.99
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.76
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.99
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4742.35
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.88
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.62
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    2.93
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4731.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.30
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.28
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000125491

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000013762

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:07.43

 All tests were passed




Server wird beendet - Lösche Semaphor 44924930.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.80
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.62
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6857.48
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.78
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.60
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907750
  j =  2                              :            46113
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.65
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17396.62
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.21
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.51
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.30
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.73
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.31
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.43
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5271.22
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.69
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.00
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.27
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.48
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12147.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.04
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999994940

Normal statistic for number of bits   :  -0.040
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.73
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000010411

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:10.32

 All tests were passed




Server wird beendet - Lösche Semaphor 45842434.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1264
p-value of test                       :    0.9968

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334384
  j =  1                              :        599997472
  j =  2                              :             1264
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.44
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.00
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.22
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908804
  j =  2                              :            45589
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908355
  j =  2                              :            45809
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17548.53
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.68
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.75
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.67
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.90
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.75
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.84
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.20
p-value of test                       :    0.9989


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.60
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.73
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.61
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    2.91
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.76
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.13
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.17
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:31.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.11
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.61
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.42
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12125.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.36
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000004471

Normal statistic for number of bits   :   0.035
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.75
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999929267

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:01.12

 All tests were passed




Server wird beendet - Lösche Semaphor 46825474.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.13
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.57
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908221
  j =  2                              :            45882
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46155
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870155
  j =  1                              :        399907692
  j =  2                              :            46151
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.90e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.95e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.10
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.00
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.32
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.98
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.36
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.64
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.10
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.35
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.21
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.76
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.73
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.30
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.85
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 2.03e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.53
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000051511

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.28
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000131029

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:08.90

 All tests were passed




Server wird beendet - Lösche Semaphor 48005122.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    4.76
p-value of test                       :  3.7e-3

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  284.96
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.92
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6899.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.24
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4804.39
p-value of test                       :    0.9910


-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46180
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870180
  j =  1                              :        399907642
  j =  2                              :            46176
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908420
  j =  2                              :            45781
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.58e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.78
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.62
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.08
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.05
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.88e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:04:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.71
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999942197

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.24
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000013537

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:15.48

 All tests were passed




Server wird beendet - Lösche Semaphor 49086466.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:05:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    3.12
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    5.85
p-value of test                       :  1.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     343
p-value of test                       :  8.0e-3

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.45
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4863.11
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:55.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907984
  j =  2                              :            45999
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908416
  j =  2                              :            45783
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.85e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.62
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.67
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.81
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.56
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.34
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.62
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.66
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.54
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.21
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3851.29
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999840779

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.35
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000002476

Normal statistic for number of bits   :   0.020
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:51.84

 All tests were passed




Server wird beendet - Lösche Semaphor 50167810.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.87
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907931
  j =  2                              :            46030
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45514
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869514
  j =  1                              :        399908980
  j =  2                              :            45498
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.28e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.28e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.21
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.61
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.34
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.31
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.43
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.24
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.25
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.35e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.76
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.01
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000121255

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.91
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999921299

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    2.54
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:15.35

 All tests were passed




Server wird beendet - Lösche Semaphor 51216386.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    3.26
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.93
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  188.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6910.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.96
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.45
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908132
  j =  2                              :            45928
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908487
  j =  2                              :            45755
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17110.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.84
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.47
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.40
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.56
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.23
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.20
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  472.53
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.93
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.42
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.75
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.32
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   91.48
p-value of test                       :  1.1e-3


-----------------------------------------------
Total number of bits:  7999801737

Normal statistic for number of bits   :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.35
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999908840

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:52.97

 All tests were passed




Server wird beendet - Lösche Semaphor 52166658.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.81
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.81
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908525
  j =  2                              :            45727
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45691
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869691
  j =  1                              :        399908623
  j =  2                              :            45681
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:31.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.09
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.86
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.90
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.90
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.01
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.52
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.96
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.39
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:13.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.97
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000035527

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.90
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000092272

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:19.56

 All tests were passed




Server wird beendet - Lösche Semaphor 53084162.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:42.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.45
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.38
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908049
  j =  2                              :            45968
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908184
  j =  2                              :            45896
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.15
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.03
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.90
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.93
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  601.04
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.60
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.18
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5238.70
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.89
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.32
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10165.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.048
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.08
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.05
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999964358

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.78
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000012826

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:43.00

 All tests were passed




Server wird beendet - Lösche Semaphor 54034434.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5580
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.44
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908288
  j =  2                              :            45856
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908331
  j =  2                              :            45827
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.52e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  116.27
p-value of test                       :  1.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.10
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   73.31
p-value of test                       :  2.4e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.33
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.99
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.65
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.88
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.21
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.85
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.55
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  187.32
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  612.53
p-value of test                       :  4.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.19
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.86
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.27
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.67
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.73
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.75
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.13
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10152.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.91
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3954.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.65
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000076639

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.20
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000033451

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           1.8e-4
 74  RandomWalk1 H (L=50, r=0)       2.4e-4
 77  RandomWalk1 J (L=1000, r=20)    4.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55083010.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1537.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.54
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908037
  j =  2                              :            45977
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907934
  j =  2                              :            46027
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.34
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.62
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.39
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.81
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.42
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.26
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.29
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  443.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.14
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.31
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10379.81
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.90
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.21
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999978095

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.11
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000025972

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:03.98

 All tests were passed




Server wird beendet - Lösche Semaphor 56098818.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9955

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.39
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.17
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46181
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870181
  j =  1                              :        399907643
  j =  2                              :            46171
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.3e-3

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.16
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17835.42
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.65
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.32
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.14
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.19
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.80
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.79
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.67
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.33e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.18e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.75e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:13.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.06
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000002173

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.05
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999904727

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:48.48

 All tests were passed




Server wird beendet - Lösche Semaphor 57147394.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9910

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  298.60
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7355.23
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.48
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.13
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908016
  j =  2                              :            45986
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908423
  j =  2                              :            45784
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.60
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.36
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.75
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.96
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.34
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.02
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.76
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.12
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.36
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.61e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.61
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.72
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.43
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12080.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999916376

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999956645

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.14
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.18

 All tests were passed




Server wird beendet - Lösche Semaphor 58163202.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:10.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   79.47
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.59
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908462
  j =  2                              :            45763
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907845
  j =  2                              :            46073
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.65e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.31e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.55
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.89
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.43
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   38.66
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  199.73
p-value of test                       :  3.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.20
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.14
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.21
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.61
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.82
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.73
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.48
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11446.34
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.47
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000117202

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.05
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999994439

Normal statistic for number of bits   :  -0.044
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.65
p-value of test                       :    0.9960

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:33.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     3.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59113474.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.90
p-value of test                       :  3.3e-3

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.71
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.86
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.11
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908077
  j =  2                              :            45957
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908840
  j =  2                              :            45574
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.72
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17205.27
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.09
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.99
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.77
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.70
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.34
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.23
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.36
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.70
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.43
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.93
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   31.63
p-value of test                       :  1.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :    2.75
p-value of test                       :  3.0e-3



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.69
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.89
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.37
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999806771

Normal statistic for number of bits   :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.70
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000052558

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:25.87

 All tests were passed




Server wird beendet - Lösche Semaphor 60162050.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4149
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6858.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.43
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5141.30
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908168
  j =  2                              :            45907
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45551
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869551
  j =  1                              :        399908906
  j =  2                              :            45535
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17151.00
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.19
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.98
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.43
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.50
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.47
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  320.61
p-value of test                       :    0.9919


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.99
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.11
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.61
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.24e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.38
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4704.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.07
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11529.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.69
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000105553

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.54
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000101359

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.20
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.45

 All tests were passed




Server wird beendet - Lösche Semaphor 61407234.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5341
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4503
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.24
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.53
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908059
  j =  2                              :            45969
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908292
  j =  2                              :            45848
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.22
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17192.78
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.05
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.49
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.70
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  421.49
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  472.02
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.05
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.80
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.05
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.16
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.35
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.90
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999889097

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.83
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000046009

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:15.64

 All tests were passed




Server wird beendet - Lösche Semaphor 62390274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.52
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.49
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  174.81
p-value of test                       :  6.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5146.75
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908194
  j =  2                              :            45897
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908173
  j =  2                              :            45909
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.48e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.62
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.91
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:33.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.84
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.56
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.89
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.98
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5179.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.95
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.13
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.46
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4979.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.81
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.45
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000077578

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.31
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999916874

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:35.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              6.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42041347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.53
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:00:47.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.51
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908354
  j =  2                              :            45814
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46171
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870171
  j =  1                              :        399907665
  j =  2                              :            46157
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.84e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.69
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17445.48
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.99
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.53
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.37
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.24
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.23
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.75
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.20
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.89
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:21.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11600.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000028555

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.41
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000055471

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:35.10

 All tests were passed




Server wird beendet - Lösche Semaphor 43778051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1488
p-value of test                       :  5.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334608
  j =  1                              :        599997024
  j =  2                              :             1488
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.82
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.43
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.01
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:33.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.38
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.28
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907867
  j =  2                              :            46062
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46156
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870156
  j =  1                              :        399907693
  j =  2                              :            46146
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.59
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.83
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.97
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.41
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.76
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.05
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.63
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.10
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.23
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.52
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.96e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.87
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:33.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.88
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.71
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.58
p-value of test                       :  7.4e-3


-----------------------------------------------
Total number of bits:  8000097249

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.87
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999919253

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:19.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44695555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7566
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.44
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1304.11
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.86
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.96
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5255.66
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45576
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869576
  j =  1                              :        399908854
  j =  2                              :            45564
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908245
  j =  2                              :            45873
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.09
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.87
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.18
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.41
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.31
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.33
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.76
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.96
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.48
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.05
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.66
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.34
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.55
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.72
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.65
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.93
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12069.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.51
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999889079

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.66
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999967862

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:32.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 J (L=50, r=25)      0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46137347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5559
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:52.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.05
p-value of test                       :  8.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    4.18
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.84
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.80
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908014
  j =  2                              :            45987
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908518
  j =  2                              :            45738
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.01e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.87
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.79
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.91
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.28
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.22
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.86
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.71
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.23
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.71
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.9909

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.78
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.09
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4650.67
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.34
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.81
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000055171

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.90
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000069904

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:12.02

 All tests were passed




Server wird beendet - Lösche Semaphor 47087619.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.57
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    3.36
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    4.07
p-value of test                       :  8.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     249
p-value of test                       :    0.9986

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.64
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1330.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7030.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.72
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908319
  j =  2                              :            45830
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45632
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869632
  j =  1                              :        399908744
  j =  2                              :            45616
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.20
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.45
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.15
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.26
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.54
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.28
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.41
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.64
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.48
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.55
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.43
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.33
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -2.40
p-value of test                       :    0.9919



-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    3.71
p-value of test                       :  1.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.02
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.64
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999905861

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.50
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000031669

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:53.68

 All tests were passed




Server wird beendet - Lösche Semaphor 48070659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7531
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.55
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45669
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869669
  j =  1                              :        399908667
  j =  2                              :            45659
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908226
  j =  2                              :            45884
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.13e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.84
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.28
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.16
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.95
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.18
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.04
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.87
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.49
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.56
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.31
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.72
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.12
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9670.27
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:19.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.41
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11457.27
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.15
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999863669

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.56
p-value of test                       :  9.1e-3


-----------------------------------------------
Total number of bits:  7999870761

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.84

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:31.47

 All tests were passed




Server wird beendet - Lösche Semaphor 49217539.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    5.43
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.26
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.44
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.20
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907979
  j =  2                              :            46006
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908258
  j =  2                              :            45859
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:29.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    4.47
p-value of test                       :  5.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9948


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.54
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.43
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    8.00
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.16
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.36
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.70
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  115.31
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.51
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.73
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.83
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.61
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.70
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.36
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.63
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.16
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.79e-5
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.25
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12412.83
p-value of test                       :  8.3e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.14
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000120373

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.21
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999991712

Normal statistic for number of bits   :  -0.066
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    2.44
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:36.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 J (L=50, r=0)       0.9995 
 100  HammingIndep, L=1200, r=25      8.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50135043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.13
p-value of test                       :    0.9996    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.29
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.54
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.19
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.19
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.82
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908473
  j =  2                              :            45756
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908297
  j =  2                              :            45847
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.76
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.85
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.64
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.25
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.18
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.37
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.31
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.11
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.81e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.93
p-value of test                       :    0.9987

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.69
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.49
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4684.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.15
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000040045

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.31
p-value of test                       :  9.5e-3


-----------------------------------------------
Total number of bits:  7999907421

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:20.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51183619.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.76
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.99
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.98
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.97
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.36
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908742
  j =  2                              :            45617
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45586
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869586
  j =  1                              :        399908833
  j =  2                              :            45576
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  6.5e-3

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.63e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.74
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.09
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.81
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.03
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.27
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.78
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  441.35
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.88
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.85
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.40e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.12
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999877781

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.30
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000034783

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:54.45

 All tests were passed




Server wird beendet - Lösche Semaphor 52297731.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:48.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.79
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.35
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.72
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45434
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869434
  j =  1                              :        399909133
  j =  2                              :            45432
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908644
  j =  2                              :            45672
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.94e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.32
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17613.66
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.20
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.29
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.54
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.26
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.05
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.41
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.36
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.05
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.26
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.84
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:20.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11566.73
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.97
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000011188

Normal statistic for number of bits   :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999978896

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:05.73

 All tests were passed




Server wird beendet - Lösche Semaphor 53379075.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.38
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.94
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908471
  j =  2                              :            45757
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907726
  j =  2                              :            46125
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.8e-3

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.96
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17167.83
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.81
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.86
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.72
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.51
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.51
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.10
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.99e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.58e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10313.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.45
p-value of test                       :  2.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:04:27.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999954821

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.82
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000185545

Normal statistic for number of bits   :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:18.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 94  HammingCorr, L = 1200           2.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54493187.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1552.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6873.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.24
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4852.55
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908291
  j =  2                              :            45853
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45943
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869943
  j =  1                              :        399908121
  j =  2                              :            45929
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.77e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.10
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.82
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.68
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.44
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.02
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.72
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.49
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9922

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.34e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.24
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.59
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.06
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.55
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.94
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.78
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999941111

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.26
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999870290

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.025
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.69
p-value of test                       :    0.9965

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:28.09

 All tests were passed




Server wird beendet - Lösche Semaphor 55574531.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7069
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.63
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.63
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.69
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.59
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.02
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908432
  j =  2                              :            45778
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.85
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.00
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.06
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.30
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.38
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.52e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.16
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.73
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.44
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.29
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999955400

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000122971

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         : 8.08e-3
p-value of test                       :    0.50

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:13.07

 All tests were passed




Server wird beendet - Lösche Semaphor 56623107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1221
p-value of test                       : 1 -  4.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334341
  j =  1                              :        599997558
  j =  2                              :             1221
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9959


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.87
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.79
p-value of test                       :  4.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:33.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  382.17
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6914.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.20
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.69
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:02.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46057
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870057
  j =  1                              :        399907887
  j =  2                              :            46055
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.74
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.13
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.94
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.55
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.49
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.94
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.13
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.98
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.24
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.92
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.97
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.46e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.81
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.91
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:11.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.22
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000060676

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999865574

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.17
p-value of test                       :    0.01

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.55e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    2.87
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:20.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  4.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57638915.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1509
p-value of test                       :  6.0e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334629
  j =  1                              :        599996982
  j =  2                              :             1509
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    4.20
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  165.03
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.78
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:57.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908076
  j =  2                              :            45959
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907747
  j =  2                              :            46122
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17383.07
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.68
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.86
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.32
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.67
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.11
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.32
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.12
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.26
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.84
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.73
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.42
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.84e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.30
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.15
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11700.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.39
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000076639

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000151864

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:26.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           6.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58687491.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.12
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.94
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.03
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:57.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45654
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869654
  j =  1                              :        399908694
  j =  2                              :            45650
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908159
  j =  2                              :            45910
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.22e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.70e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.36
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17342.97
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.44
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.88
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.39
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.18
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    2.50
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.24
p-value of test                       :    0.9962

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12222.51
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.52
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000030784

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.66
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000013771

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:32.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59736067.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5569
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:05:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.53
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.98
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.57
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.62
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.18
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45532
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869532
  j =  1                              :        399908939
  j =  2                              :            45526
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908151
  j =  2                              :            45917
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.49e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.53
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17472.62
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.22
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.77
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.54
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.88
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.50
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.39
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.83
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.51
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.68
p-value of test                       :    0.9974


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.42e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.06
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.96
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000013345

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.34
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999835091

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:09.62

 All tests were passed




Server wird beendet - Lösche Semaphor 60784643.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.66
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:17.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1588.45
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.67
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.43
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908399
  j =  2                              :            45796
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908272
  j =  2                              :            45858
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.44e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.53
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.60
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.99
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.11
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.59
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.87
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.45
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.40
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.39
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4744.04
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.09
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.89
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.89
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.68
p-value of test                       :    0.9964

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.68
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.05
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.52
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000027217

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.14
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000064624

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.010
p-value of test                       :    0.50

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:20.64

 All tests were passed




Server wird beendet - Lösche Semaphor 61833219.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9915

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.96
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.07
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.60
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:54.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908467
  j =  2                              :            45765
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908192
  j =  2                              :            45895
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   10.22
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17333.40
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.56
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.49
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.03
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.12
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.90
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:32.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.85
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.40
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.05e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.68
p-value of test                       :    0.9964

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.11
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.22
p-value of test                       :    0.9965

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.91
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.96
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.27
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000156079

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.46
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999890237

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   02:58:48.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 65  SumCollector                    0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62881795.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:01.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.32
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.37
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.18
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45508
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869508
  j =  1                              :        399908986
  j =  2                              :            45504
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45355
p-value of test                       :    0.9929


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869355
  j =  1                              :        399909293
  j =  2                              :            45349
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 3.49e-4
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.27
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.23
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.12
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.84
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.47
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.95
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.36
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.04
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.94
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.31
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.06
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9817.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.37
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999750380

Normal statistic for number of bits   :   -1.97
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.19
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000074371

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.27
p-value of test                       :    0.99

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:49.37

 All tests were passed




Server wird beendet - Lösche Semaphor 42074116.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4510
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     560
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.20
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.43
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4915.46
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45449
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869449
  j =  1                              :        399909105
  j =  2                              :            45443
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45431
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869431
  j =  1                              :        399909140
  j =  2                              :            45427
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9930


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    : 9.78e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.31
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.76e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.09
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.50
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.57
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.60
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.40
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.08
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.09
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.85
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.18
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.063
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:19.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11505.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.11
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999936455

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.76
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000000487

Normal statistic for number of bits   : 3.85e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:38.88

 All tests were passed




Server wird beendet - Lösche Semaphor 43745284.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.07
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7092.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.20
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.36
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.80
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46253
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870253
  j =  1                              :        399907499
  j =  2                              :            46243
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908028
  j =  2                              :            45980
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.62e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.13e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.87
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.68
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.61
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.40
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.57
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.86
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.35
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.06
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.25
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.85e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.66
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.02
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11665.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.74
p-value of test                       :    0.9902


-----------------------------------------------
Total number of bits:  8000038062

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.71
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000074104

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.81

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:15.98

 All tests were passed




Server wird beendet - Lösche Semaphor 44662788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1231
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334351
  j =  1                              :        599997538
  j =  2                              :             1231
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.72
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7102.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.69
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    : 3.90e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.45
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.22
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4898.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908711
  j =  2                              :            45640
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908122
  j =  2                              :            45936
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-5
p-value of test                       : 1 -  5.0e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  185.77
p-value of test                       :  9.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17098.18
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.15
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.34
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.92
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.66
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.73
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.59
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.75e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.15e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.02
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.23
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.31
p-value of test                       :  6.4e-3


-----------------------------------------------
Total number of bits:  7999957473

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.96
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999955094

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.52
p-value of test                       :  5.8e-3

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:31.02
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9999 
 72  Savir2                          9.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45580292.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.71
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.03
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.11
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908356
  j =  2                              :            45822
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908290
  j =  2                              :            45846
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.63e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17118.27
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.76
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.87
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.03
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.10
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.99
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.44
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.88
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.51
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.99
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11492.65
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.83
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999949874

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.39
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000035239

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:54.80

 All tests were passed




Server wird beendet - Lösche Semaphor 46432260.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.61
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.82
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.94
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.92
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.78
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908611
  j =  2                              :            45693
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908704
  j =  2                              :            45642
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.18e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : 2.31e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.49
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.02
p-value of test                       :  6.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.63
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.17
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.95
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.79
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.62
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.25
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.27
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.64
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.56
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.33
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.51
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.67
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.75
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3975.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.30
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999915569

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.12
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999936953

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:42.85

 All tests were passed




Server wird beendet - Lösche Semaphor 47349764.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1225
p-value of test                       : 1 -  6.7e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334345
  j =  1                              :        599997550
  j =  2                              :             1225
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.41
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.21
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.03
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:56.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908669
  j =  2                              :            45652
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908781
  j =  2                              :            45605
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17349.05
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.10
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.68
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.75
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.70
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.13
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.28
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  251.82
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.60
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999902753

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.70
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999957563

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.53
p-value of test                       :  5.7e-3

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:50.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  6.7e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48431108.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9919


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    3.61
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.89
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.56
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:56.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45583
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869583
  j =  1                              :        399908837
  j =  2                              :            45577
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908011
  j =  2                              :            45987
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.15e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.98
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.14
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16969.85
p-value of test                       :    0.9935



-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.79
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.29
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.27
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.71
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.76
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.32
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.64
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.26
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.93e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.99
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.58
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.09
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999921584

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.52
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000063442

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.21
p-value of test                       :  7.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.52
p-value of test                       :    0.9941

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:05.18

 All tests were passed




Server wird beendet - Lösche Semaphor 49709060.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.24
p-value of test                       :  7.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9919

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.49
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908136
  j =  2                              :            45923
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45933
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869933
  j =  1                              :        399908141
  j =  2                              :            45919
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-5
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17184.90
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.99
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.31
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.15
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.76
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.67
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.98
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.81
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.10
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.88
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.93
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.30
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    2.37
p-value of test                       :  8.9e-3



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.58e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.17
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.64
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999828536

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.39
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000063061

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:57.82

 All tests were passed




Server wird beendet - Lösche Semaphor 50659332.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9924

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9933

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.85
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6839.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.87
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.09
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:53.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908843
  j =  2                              :            45577
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907978
  j =  2                              :            46002
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17064.72
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.89
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.89
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.79
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.53
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.49
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  200.74
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.97
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.42
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.31
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.74
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.25
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10134.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4801.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.37
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999919139

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.28
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999907823

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:11.29

 All tests were passed




Server wird beendet - Lösche Semaphor 51642372.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.41
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.03
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4877.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908173
  j =  2                              :            45912
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908089
  j =  2                              :            45948
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.81e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.95
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.88
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.09
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.76
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.68
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.80
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.94e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.44e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.39
p-value of test                       :  2.9e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.42
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000088258

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.31
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000007129

Normal statistic for number of bits   :   0.056
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.25e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.2e-3

Anderson-Darling statistic = A2       :    5.87
p-value of test                       :  1.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.20
p-value of test                       :  6.9e-4    *****

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.22
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 105  AutoCor, d=1, r=27              6.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52625412.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.30
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908075
  j =  2                              :            45961
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908021
  j =  2                              :            45982
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.01e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.88e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -3.10
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.44
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.86
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.24
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.60
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.08
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.60
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.23
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.73
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.88
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:19.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.58
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000101638

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.59
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000029893

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.23
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 57  AppearanceSpacings, r = 0       0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53673988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.99
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    4.10
p-value of test                       :  7.8e-3

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.03
p-value of test                       :  2.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.48
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.85
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.21
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908120
  j =  2                              :            45934
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908293
  j =  2                              :            45846
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.16e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.064
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.9e-4    *****

Anderson-Darling statistic = A2       :    5.34
p-value of test                       :  2.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17959.29
p-value of test                       :  2.5e-3



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.94
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.02
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.25
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.01
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.15
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4774.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.29
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.68
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.42
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.32
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.68
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9757.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9810.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:04:19.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5070.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.72
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.45
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000016729

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.02
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000007816

Normal statistic for number of bits   :   0.062
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:12.26

 All tests were passed




Server wird beendet - Lösche Semaphor 54722564.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.87
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6979.16
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908477
  j =  2                              :            45760
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908394
  j =  2                              :            45794
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.55
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   14.04
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  173.59
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17548.40
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.92
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.50
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.67
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.16
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.43
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.50
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.11
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.63
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.33
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.3e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.94e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999962012

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.84
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000181036

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.13
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55738372.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4530
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.72
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5196.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45531
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869531
  j =  1                              :        399908940
  j =  2                              :            45527
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46115
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870115
  j =  1                              :        399907771
  j =  2                              :            46113
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.09
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.68
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17487.74
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.55
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.71
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.67
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.56
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.33
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.25
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.85
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.59
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.68e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.40
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.11
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:19.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.86
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999960617

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.32
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999927629

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:15.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56754180.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5278
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.14
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.08
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.34
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.20
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:19.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.68
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46422
p-value of test                       :  5.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870422
  j =  1                              :        399907160
  j =  2                              :            46414
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46208
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870208
  j =  1                              :        399907589
  j =  2                              :            46198
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.10e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9926


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.58e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.95
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.35
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.01
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.44
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.36
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.57
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.37
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.58
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.92
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.04
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.88
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.84
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.51
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.76
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000004873

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.39
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999892115

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:34.38

 All tests were passed




Server wird beendet - Lösche Semaphor 57769988.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.69
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.11
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908316
  j =  2                              :            45839
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908659
  j =  2                              :            45666
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.40e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.17
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.16
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.48
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.02
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.74
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.42
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:51.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.08
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.86
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.40
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.74
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.80
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.74
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10265.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.88
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:04:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11485.84
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.05
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999982619

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.20
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999962540

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.062
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:52.62

 All tests were passed




Server wird beendet - Lösche Semaphor 58884100.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4190
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    5.32
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.29
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.45
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5147.77
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908133
  j =  2                              :            45923
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908373
  j =  2                              :            45809
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.89e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.67e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.41
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.95
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.83
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.15
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.28
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5312.39
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.19
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  463.72
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.43
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.71
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.19
p-value of test                       :  4.6e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.41
p-value of test                       :  8.9e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999997559

Normal statistic for number of bits   :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.97
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000008005

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:05.18

 All tests were passed




Server wird beendet - Lösche Semaphor 59932676.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.23
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6898.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.75
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.11
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907735
  j =  2                              :            46119
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907882
  j =  2                              :            46053
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.76e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9971


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.12e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.85
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.40
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.71
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.06
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.34
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.39
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.12
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.30
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.13
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.20e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.52
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.88
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000193489

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.01
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999830582

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:42.70

 All tests were passed




Server wird beendet - Lösche Semaphor 60915716.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.35
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.54
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:21.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908198
  j =  2                              :            45895
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908207
  j =  2                              :            45895
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:31.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.39
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.46
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17458.85
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.38
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.92
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.94
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  427.40
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.31
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.50
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.36
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.51
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.70e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.74
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5124.60
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.24
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000261040

Normal statistic for number of bits   :    2.06
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.68
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000005947

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:38.45

 All tests were passed




Server wird beendet - Lösche Semaphor 62062596.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.35
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.20
p-value of test                       :  7.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    3.35
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.39
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.52
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45678
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869678
  j =  1                              :        399908650
  j =  2                              :            45666
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908522
  j =  2                              :            45730
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.60e-4
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17634.11
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.40
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.43
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.93
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.62
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.63
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.48
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.49
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.65
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.13
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.45
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.39
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.06
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.66
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.038
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.21
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999818564

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.15
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999968924

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:50.07

 All tests were passed




Server wird beendet - Lösche Semaphor 42106885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7500
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    4.02
p-value of test                       :  8.5e-3

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.34
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.19
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908713
  j =  2                              :            45636
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908451
  j =  2                              :            45770
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.98
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.92
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.69
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.07
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.24
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.03
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.28
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.45
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.24
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.11
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.05
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.59
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:47.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.20
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4295.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4323.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11485.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.45
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000013045

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000172414

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:09.05

 All tests were passed




Server wird beendet - Lösche Semaphor 43909125.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:14.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   88.62
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.10
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.62
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908701
  j =  2                              :            45642
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908101
  j =  2                              :            45948
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 9.20e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.42
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.63
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.64
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.57
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.66
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.89
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.62
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.83
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.95
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.19
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.30
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.60
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.29
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5094.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.71
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999932141

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.98
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999947096

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    2.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:02.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44761093.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5288
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4133
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.56
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7200.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.70
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46268
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870268
  j =  1                              :        399907465
  j =  2                              :            46266
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908613
  j =  2                              :            45692
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  3.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
p-value of test                       :  9.9e-3

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.10
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.01
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.37
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.67
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.33
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.73
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.71
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.28
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.86
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.48
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.48
p-value of test                       :    0.9911


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.71
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:32.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.43
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000346318

Normal statistic for number of bits   :    2.74
p-value of test                       :  3.1e-3



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.65
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999857624

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:27.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 14  BirthdaySpacings, t = 3         0.9991 
 26  SimpPoker, r = 0                0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45645829.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.64
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.88
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  168.37
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.32
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908336
  j =  2                              :            45826
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908146
  j =  2                              :            45915
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17712.28
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.40
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.55
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.81
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.33
p-value of test                       :  7.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.27
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.15
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.72
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.44
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.73
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.12
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.82
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3927.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11557.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.76
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999983303

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.99
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999958448

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:36.78

 All tests were passed




Server wird beendet - Lösche Semaphor 46792709.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  175.23
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.35
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.57
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.29
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:56.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908287
  j =  2                              :            45855
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907789
  j =  2                              :            46095
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.45e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.22e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.28
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17241.68
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.30
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.98
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.54
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.18
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.77
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.28
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12017.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.95
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999976775

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.16
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999956480

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:49.23

 All tests were passed




Server wird beendet - Lösche Semaphor 47710213.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7564
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9989

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     187
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.46
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.50
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.73
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908468
  j =  2                              :            45760
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908029
  j =  2                              :            45981
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.25e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.061
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.22
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.66
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.87
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.92
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.12
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.64
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.25
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.37
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.75
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.08
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:19.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.69
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.39
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999889340

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.85
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000007987

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.64

 All tests were passed




Server wird beendet - Lösche Semaphor 48889861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4545
p-value of test                       :  8.7e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     533
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.54
p-value of test                       :  5.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.81
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.00
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  158.98
p-value of test                       :  8.4e-3


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.32
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:55.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908495
  j =  2                              :            45751
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46269
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870269
  j =  1                              :        399907467
  j =  2                              :            46259
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.22
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17280.28
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.67
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.24
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.62
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.32
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4845.67
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.07
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.40
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.79
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.18
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4320.58
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.46
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999962360

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.53
p-value of test                       :  7.5e-3


-----------------------------------------------
Total number of bits:  7999882731

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:03.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         8.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49807365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1236
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334356
  j =  1                              :        599997528
  j =  2                              :             1236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.76
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.49
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.89
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.24
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907834
  j =  2                              :            46074
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908069
  j =  2                              :            45964
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:32.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    : 9.15e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.57
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.76e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.57e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.96
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.56
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.80
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.89
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.69
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.71
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.68
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.26
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.85
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.79
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.96
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.23
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -2.02
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.69
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.52
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999893900

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.18
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000034927

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:41.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2            0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50724869.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5487
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:54.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908877
  j =  2                              :            45551
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908071
  j =  2                              :            45960
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.20
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.69
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.95
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.17
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.70
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    2.85
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.62e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.95
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.81
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12075.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.98
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000082471

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.38
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999872321

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.32

 All tests were passed




Server wird beendet - Lösche Semaphor 51707909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9934

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    4.67
p-value of test                       :  4.1e-3

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.62
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.16
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.78
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908285
  j =  2                              :            45856
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908626
  j =  2                              :            45684
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:30.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984


-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.11
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.96
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.63
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.09
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.88
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.59
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.76
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.89
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.82
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.79
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.81
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.44
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4329.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.33
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000022366

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000010414

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:07.21

 All tests were passed




Server wird beendet - Lösche Semaphor 52690949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9935


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.16
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.35
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:41.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   98.48
p-value of test                       :  2.1e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.40
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.89
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4869.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:55.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46100
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870100
  j =  1                              :        399907803
  j =  2                              :            46094
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908524
  j =  2                              :            45729
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.38e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.15
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.12
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.02
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.91
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.00
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.63
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4784.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.03
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.08
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-4
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9664.76
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5003.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.92
p-value of test                       :  6.9e-3


-----------------------------------------------
Total number of bits:  7999776660

Normal statistic for number of bits   :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.95
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999888401

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:51.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          2.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53706757.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     345
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.00
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.62
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.29
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.21
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:58.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908191
  j =  2                              :            45900
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908756
  j =  2                              :            45622
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17206.72
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.34
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.00
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.21
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.65
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.70
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  308.13
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.28
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.23
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.84
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -2.36
p-value of test                       :    0.9908



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :-2.11e-16
p-value of test                       :    0.50

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.76
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.99
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.55
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    4.97
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10429.83
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.17
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999927794

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.23
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000119824

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.54
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:04.18

 All tests were passed




Server wird beendet - Lösche Semaphor 54755333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:04:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.05
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1344.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:22.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.83
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.17
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.67
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908677
  j =  2                              :            45657
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907753
  j =  2                              :            46122
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 3.29e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17199.59
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.28
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.99
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.91
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.54
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.45
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.73
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.32
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 4.71e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10279.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:33.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11563.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.44
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999886076

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.67
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999989183

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:47.75

 All tests were passed




Server wird beendet - Lösche Semaphor 55803909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.25
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.75
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45950
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869950
  j =  1                              :        399908102
  j =  2                              :            45946
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907667
  j =  2                              :            46162
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.67
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.04
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.15
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.24
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.40
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4882.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.53
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.35
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.96
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.67
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.06
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000109759

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.83
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000041128

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.01

 All tests were passed




Server wird beendet - Lösche Semaphor 56885253.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4173
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9953

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.45
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908641
  j =  2                              :            45672
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46006
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870006
  j =  1                              :        399907991
  j =  2                              :            46000
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.15e-5
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.72
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.84
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.31
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  563.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   91.71
p-value of test                       :    0.9987


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.68
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.72
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.91
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.97
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.82
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.69
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.39
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.48
p-value of test                       :    0.9934

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.01e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.15
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.02
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999945158

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.31
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999877088

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.93

 All tests were passed




Server wird beendet - Lösche Semaphor 57933829.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7150
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:51.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.88
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.03
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908828
  j =  2                              :            45577
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45416
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869416
  j =  1                              :        399909170
  j =  2                              :            45412
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.45
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.76
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.88
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.40
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.98
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.72
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.94
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.86
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.10
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.95
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.47
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.84
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000046585

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.32
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999967430

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:43.01

 All tests were passed




Server wird beendet - Lösche Semaphor 58949637.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4200
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     347
p-value of test                       :  4.3e-3

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7218.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907964
  j =  2                              :            46006
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907918
  j =  2                              :            46035
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17468.69
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.61
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.20
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.37
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.64
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.11
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.01
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.36
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.83
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12049.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.92
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999992639

Normal statistic for number of bits   :  -0.058
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.61
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000124948

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:10.22

 All tests were passed




Server wird beendet - Lösche Semaphor 60096517.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:14.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.53
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.79
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908155
  j =  2                              :            45918
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45505
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869505
  j =  1                              :        399908992
  j =  2                              :            45501
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.30e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.28e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.25
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.37
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.05
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.96
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.62
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.59
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.50
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    2.84
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.04
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.053
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.84
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999935858

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.53
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999936842

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.058
p-value of test                       :    0.52

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.11
p-value of test                       : 1 -  6.7e-5    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:57.62

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997267
  j =  2                              :             1365
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.33
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.13
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.53
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.81
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.32
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908907
  j =  2                              :            45539
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908038
  j =  2                              :            45978
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9972

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  9.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.00e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.98e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.92
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.23
p-value of test                       :    0.9900


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.97
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.37
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.49
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.62
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.78
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.82
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5126.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.91
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.20
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.53
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    : 3.49e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    5.09
p-value of test                       :  2.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.93
p-value of test                       :    0.9983

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.16
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000048304

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.57
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000042766

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:03:42.93

 All tests were passed




Server wird beendet - Lösche Semaphor 62423045.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    4.94
p-value of test                       :  3.1e-3

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.66
p-value of test                       :  4.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     121
p-value of test                       :    0.9916

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  193.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.40
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:03:02.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907738
  j =  2                              :            46131
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908463
  j =  2                              :            45767
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:31.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 3.80e-4
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.28
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.09
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.99
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.20
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.58
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.66
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.47
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.85
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.54
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.38
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.97
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:16.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.35
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:13.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10228.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9793.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:20.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4350.34
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12064.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.67
p-value of test                       :    0.9934


-----------------------------------------------
Total number of bits:  8000089908

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.99
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999917549

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:21.79

 All tests were passed




Server wird beendet - Lösche Semaphor 42139654.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:53.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:12.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.38
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.56
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1523.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.51
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.83
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:00.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.94e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17173.84
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.68
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.08
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.45
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.54
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.83
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.90e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.23
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.77
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.23
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999962834

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.40
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000056623

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:26.69

 All tests were passed




Server wird beendet - Lösche Semaphor 43155462.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7561
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7108.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.07
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45513
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869513
  j =  1                              :        399908979
  j =  2                              :            45503
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45630
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869630
  j =  1                              :        399908742
  j =  2                              :            45626
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-4
p-value of test                       :  2.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 1.01e-5
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    8.19
p-value of test                       :  9.7e-5    *****

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.02
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17674.38
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.80
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.19
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.05
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.48
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.03
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.96
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.82
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.46
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999944354

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.79
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000119506

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.18
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:17:22.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              9.7e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44072966.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.47
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.49
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.99
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908422
  j =  2                              :            45783
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908695
  j =  2                              :            45651
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.83e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.39
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.89
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.11
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17559.82
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.80
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.61
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.59
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.63
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.94
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.76
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.35
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.83
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.58
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.21
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.17
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.13
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:40.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.30
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.11
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.22
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000040966

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.87
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000090244

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:49.40

 All tests were passed




Server wird beendet - Lösche Semaphor 46071814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5295
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.06
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5083.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908154
  j =  2                              :            45920
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907799
  j =  2                              :            46093
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.01e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.17
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.81
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.21
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.06
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.23
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.07
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.26
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.08
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.79
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.39
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5209.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.79
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.57
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.13
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.93
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.34
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.71e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.26
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.18
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10247.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  2.7e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    6.35
p-value of test                       :  7.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4584.63
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.90
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000075508

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.31
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999961085

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:08.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 95  HammingIndep, L=30, r=0         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47153158.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    5.23
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.81
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.75
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.58
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:57.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907907
  j =  2                              :            46045
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908316
  j =  2                              :            45836
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.84e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.18
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.69
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.74
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.13
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.21
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.53
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.43
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.90
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.15
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.90
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.19
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4665.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.17
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.53
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000124189

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.24
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999895811

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:15.42

 All tests were passed




Server wird beendet - Lösche Semaphor 48168966.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5293
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.73
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4873.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908027
  j =  2                              :            45979
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908042
  j =  2                              :            45973
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.63
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.23
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.12
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.10
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.80
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.33
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.67
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.75
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.93
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.97
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.00e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.76e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.31
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9898.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -7.81e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11749.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.23
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000121234

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.38
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000081889

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.51

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:36.30

 All tests were passed




Server wird beendet - Lösche Semaphor 49152006.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.64
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    4.34
p-value of test                       :  6.0e-3

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.38
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.90
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.35
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.72
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:59.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907746
  j =  2                              :            46124
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908177
  j =  2                              :            45901
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.60e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.60e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -4.24e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.57
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.30
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.44
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17222.01
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.43
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.19
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.12
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.33
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.64
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.78
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.34
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.70
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.53
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.22
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.62
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.41
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.64
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.18e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.59
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000021889

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.57
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999935003

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.80

 All tests were passed




Server wird beendet - Lösche Semaphor 50102278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.81
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4769.38
p-value of test                       :    0.9968


-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908616
  j =  2                              :            45689
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907734
  j =  2                              :            46130
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:32.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-4
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    : 7.25e-6
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.30e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.00
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.71
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.90
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.99
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.80
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.28
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.94
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.32
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.24
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.19
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.10
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.19e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.29
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:12.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.9925

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4672.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11618.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.73
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999912797

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.74
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000148207

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:38.30

 All tests were passed




Server wird beendet - Lösche Semaphor 51118086.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    3.92
p-value of test                       :  9.5e-3

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.25
p-value of test                       :  2.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.79
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1539.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7148.29
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.97
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908221
  j =  2                              :            45888
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.9920

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.18
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.91
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.79
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.64
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.73
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.54
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000123850

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.43
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999944057

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.035
p-value of test                       :    0.51

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:53.38

 All tests were passed




Server wird beendet - Lösche Semaphor 52232198.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5266
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:11.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.59
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.56
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.18
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.77
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908028
  j =  2                              :            45980
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45491
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869491
  j =  1                              :        399909022
  j =  2                              :            45483
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.63
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.55
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.19
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.51
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.76
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.76
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.34
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.61
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.32
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.81
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9532.87
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9889.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.52
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999967382

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.09
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000033040

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:11.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 90  HammingWeight2, r = 0           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53182470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    3.59
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     661
p-value of test                       :  7.4e-3

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    3.21
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:17.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.03
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.51
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5130.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908390
  j =  2                              :            45799
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908762
  j =  2                              :            45607
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-4
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 3.62e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.76
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.06
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.52
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5169.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.55
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.30
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.15e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.22
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.92
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.65
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4719.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.24
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11707.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.96
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000015445

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.16
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999930650

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:12.79

 All tests were passed




Server wird beendet - Lösche Semaphor 54231046.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1571.20
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.76
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45469
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869469
  j =  1                              :        399909067
  j =  2                              :            45459
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908256
  j =  2                              :            45869
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  5.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.97e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.81
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.49
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.22
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.33
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.57
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.78
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.34
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.88
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.48
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.51
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.49
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.55
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000012565

Normal statistic for number of bits   :   0.099
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.32
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999967409

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.78

 All tests were passed




Server wird beendet - Lösche Semaphor 55279622.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7072
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.42
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.53
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.58
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.66
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.22
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.98
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45801
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869801
  j =  1                              :        399908401
  j =  2                              :            45795
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45435
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869435
  j =  1                              :        399909135
  j =  2                              :            45425
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 3.00e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17508.65
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.44
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.68
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.84
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.06
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.15
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.84
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.21
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.94e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.48
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12076.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.05
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.50
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000124189

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.90
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999947960

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9993    *****

Tests on the sum of all N observations
Standardized normal statistic         :  -0.081
p-value of test                       :    0.53

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    2.64
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:16.76

 All tests were passed




Server wird beendet - Lösche Semaphor 56262662.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.41
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.33
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45521
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869521
  j =  1                              :        399908959
  j =  2                              :            45519
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907836
  j =  2                              :            46076
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.22e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.16
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.60
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17561.86
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.13
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.70
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.00
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.91
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.09
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.39
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.04
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.35
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.77
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.45
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4760.87
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.02
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.23
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.81
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.03
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.68
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.23
p-value of test                       :  2.6e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.36
p-value of test                       :    0.9908



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 7.35e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:41.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.76
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000033640

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.64
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999955667

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:45.48

 All tests were passed




Server wird beendet - Lösche Semaphor 57278470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9919

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.41
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.09
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.04
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:00.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907748
  j =  2                              :            46120
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908683
  j =  2                              :            45654
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.93
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.06
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.97
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.97
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.14
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.34
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.96
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.10
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.41
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.77
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.29
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999863675

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.01
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999913943

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:09.50

 All tests were passed




Server wird beendet - Lösche Semaphor 58359814.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7576
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.94
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.51
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.18
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.90
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.49
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908173
  j =  2                              :            45903
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46202
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870202
  j =  1                              :        399907600
  j =  2                              :            46194
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.82e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -4.58e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17584.57
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.47
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.47
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.81
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.57
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.67
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.75
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10207.87
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.59
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999826670

Normal statistic for number of bits   :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.04
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999967559

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:53.23

 All tests were passed




Server wird beendet - Lösche Semaphor 59473926.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.76
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.85
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.93
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.31
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907874
  j =  2                              :            46060
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.39e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.15
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.31
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.26
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.39
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.21
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.72
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.47
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.98
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.04
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.79
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.14
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.03
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.96
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.50e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.03
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.90
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.57
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:19.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3893.91
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.81
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999824027

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.35
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000032317

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:32.44

 All tests were passed




Server wird beendet - Lösche Semaphor 60456966.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  293.81
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1573.34
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.07
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.87
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.55
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908380
  j =  2                              :            45807
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.00
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.21
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.33
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17223.22
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.37
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.56
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.86
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.35
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   40.20
p-value of test                       :    0.9995    *****


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.45
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.52
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.95
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.03
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.07
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.38e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.80
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.08
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999957932

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.69
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999761798

Normal statistic for number of bits   :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:14.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61440006.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.85
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.77
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6775.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.65
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.04
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907997
  j =  2                              :            45991
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45736
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869736
  j =  1                              :        399908531
  j =  2                              :            45730
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:29.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.78e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.85
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17297.66
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.26
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.88
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.41
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.67
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.26
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5076.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.93
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.40
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.70
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10267.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:29.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12108.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.44
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999872273

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.59
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999888164

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:15.93

 All tests were passed




Server wird beendet - Lösche Semaphor 62521350.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5583
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     973
p-value of test                       :  8.4e-3

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.77
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.49
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.25
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908514
  j =  2                              :            45734
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45506
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869506
  j =  1                              :        399908990
  j =  2                              :            45502
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.88
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.72
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17110.87
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.98
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.69
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.12
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.45
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.07
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.17
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.18
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.11
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.03
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.99
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:34.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.80
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.70
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.27
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3991.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.42
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.20
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000010774

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.68
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000047170

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:25:50.63

 All tests were passed




Server wird beendet - Lösche Semaphor 42172423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4079
p-value of test                       : 1 -  4.0e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.11
p-value of test                       : 1 -  9.9e-5    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.63
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.48
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.59
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907756
  j =  2                              :            46116
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45524
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869524
  j =  1                              :        399908957
  j =  2                              :            45514
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.86
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.39
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.72
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.69
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.38
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.45
p-value of test                       :  8.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.93
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.50
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.18
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.05
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.03
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9766.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.11
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000133327

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.67
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000090274

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:44.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7        1 -  4.0e-5
 24  ClosePairs mNP1, t = 9         1 -  9.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44040199.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5295
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7581
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:41.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.69
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  386.85
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.61
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.77
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908736
  j =  2                              :            45623
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907856
  j =  2                              :            46069
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  4.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.08e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -8.46e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.44
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.84
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.71
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.56
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.27
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.41
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.49
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5214.38
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.24
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.15
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.27e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.28
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.69
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000058822

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.53
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000081694

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.70

 All tests were passed




Server wird beendet - Lösche Semaphor 45056007.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.47
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1306.02
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46165
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870165
  j =  1                              :        399907673
  j =  2                              :            46159
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45518
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869518
  j =  1                              :        399908967
  j =  2                              :            45512
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    5.17
p-value of test                       :  2.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  2.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17265.47
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.39
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.43
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.15
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.94
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.72
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.40
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4780.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.07
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.75
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.29
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.24e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.38
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.12
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.64
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000101287

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.76
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000086842

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-3
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:05.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 92  HammingCorr, L = 30             0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46006279.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:52.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9963

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.44
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.77
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.83
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.13
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4859.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:01.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908525
  j =  2                              :            45733
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908885
  j =  2                              :            45553
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.23
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   71.64
p-value of test                       :  5.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.65
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.13
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.69
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.84
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.63
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.63
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.29
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.90
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  460.23
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.97
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.07
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.05
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10171.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.01
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000021085

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000110305

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:27.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 62  WeightDistrib, r = 0            5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46989319.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5380
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     832
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.42
p-value of test                       :  7.1e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.49
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.35
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.59
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.73
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907708
  j =  2                              :            46143
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908222
  j =  2                              :            45886
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.20e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   91.82
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17726.12
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.27
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.12
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.57
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.49
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.63
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.93
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.78
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.47
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.62
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.40e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:18.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.79
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11644.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:33.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.76
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000069232

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.31
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000041401

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.094
p-value of test                       :    0.54

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:55.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP, t = 16          7.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47972359.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.64
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.16
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.89
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:01.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908223
  j =  2                              :            45887
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908267
  j =  2                              :            45859
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9912


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :  1.4e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 1.25e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    7.15
p-value of test                       :  3.0e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9998    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17466.63
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.31
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.98
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.04
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.73
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.14
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.54
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.51
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.16
p-value of test                       :    0.9970

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9661.95
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5035.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4363.99
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999993773

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.10
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000203320

Normal statistic for number of bits   :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         : -7.82e-3
p-value of test                       :    0.50

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:49.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft, t = 24                  0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48922631.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.79
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.32
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.42
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:54.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45879
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869879
  j =  1                              :        399908244
  j =  2                              :            45875
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908614
  j =  2                              :            45687
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.01e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.35
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17239.46
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.83
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.43
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.54
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.57
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.79
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.60
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.57
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.85
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.54
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.63
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.52
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.69
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999989204

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.18
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999959588

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.42

 All tests were passed




Server wird beendet - Lösche Semaphor 49872903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1495
p-value of test                       :  2.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334615
  j =  1                              :        599997010
  j =  2                              :             1495
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6906.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.70
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907764
  j =  2                              :            46112
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908452
  j =  2                              :            45768
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.70
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.89
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17410.89
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.43
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.48
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.44
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.35
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.96
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.35
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.58
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.66
p-value of test                       :  6.2e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.43e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.36
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9741.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:04:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.67
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999940631

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.66
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000039226

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.20
p-value of test                       :    0.01

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:22.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50823175.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.68
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908410
  j =  2                              :            45789
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908776
  j =  2                              :            45609
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.69
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.19
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.32
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.64
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.39
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.92
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.21
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.33
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.93
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.85e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.70
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.54
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.93
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.96
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.24
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000146518

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999968078

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.096
p-value of test                       :    0.54

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:53.59

 All tests were passed




Server wird beendet - Lösche Semaphor 52068359.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.16
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.20
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.58
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5225.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908519
  j =  2                              :            45730
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.98
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17023.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.91
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.32
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.57
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.98
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.86
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.40
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4758.90
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  476.45
p-value of test                       :  4.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.26
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.24
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.56
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.38
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999954797

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.81
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999967070

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.068
p-value of test                       :    0.47

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:11.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   4.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53018631.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.22
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.46
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6815.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.58
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908325
  j =  2                              :            45836
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907756
  j =  2                              :            46116
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:30.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.40e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.38
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   62.49
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.94
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.25
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.47
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.61
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.75
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.29
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.90
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.42
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.78
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.00
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:47.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.64
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.47
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999997841

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.76
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000005746

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:08.94

 All tests were passed




Server wird beendet - Lösche Semaphor 53968903.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5310
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.50
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     532
p-value of test                       :    0.9975

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1331.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.57
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.10
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.16
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908006
  j =  2                              :            45985
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908133
  j =  2                              :            45929
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.94e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -3.97e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17339.64
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.56
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.68
p-value of test                       :    0.9924


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.63
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.06
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.02
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.51
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.16
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.82
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.44
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9780.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.51
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999934103

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.64
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999878786

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:21.86

 All tests were passed




Server wird beendet - Lösche Semaphor 55050247.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.21
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.58
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6939.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.89
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.91
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908234
  j =  2                              :            45880
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908018
  j =  2                              :            45988
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9940


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.95
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.85
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.75
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.97
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.73
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.66
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.10
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.01
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.30
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.43
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.79
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.24
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  258.66
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.17
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:17.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.13
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000033880

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999904655

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:46.00

 All tests were passed




Server wird beendet - Lösche Semaphor 56164359.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.99
p-value of test                       :  8.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     547
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.48
p-value of test                       :  5.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.52
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.83
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.36
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.18
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45480
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869480
  j =  1                              :        399909045
  j =  2                              :            45470
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908049
  j =  2                              :            45971
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.19
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.05
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.45
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.77
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.62
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.70
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.18
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.03
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.09
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.77
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.10
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.65
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.57
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.37
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  : -5.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.02e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11530.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.31
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999993920

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.22
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000027493

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:35.00

 All tests were passed




Server wird beendet - Lösche Semaphor 57212935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:09.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.97
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907977
  j =  2                              :            46004
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45553
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869553
  j =  1                              :        399908895
  j =  2                              :            45551
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.03e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.69
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.20
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.08
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.47
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.99
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.01
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.36
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.77
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.68
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.55
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.59
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.05
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.75
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.95
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.09
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.15
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9871.20
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999953189

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.33
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000127582

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:23.09

 All tests were passed




Server wird beendet - Lösche Semaphor 58261511.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.21
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.99
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.93
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6871.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.46
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.18
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:29.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908187
  j =  2                              :            45902
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907932
  j =  2                              :            46025
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.15e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.60
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.04
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.23
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.67
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.37
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.31
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.54
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5121.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  159.03
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.29
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.42
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.17
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.35
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.00
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.53
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.59
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10257.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:39.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.80
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999961157

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999967067

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:24.18

 All tests were passed




Server wird beendet - Lösche Semaphor 59375623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1375.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.98
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.37
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907832
  j =  2                              :            46081
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908123
  j =  2                              :            45934
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.21e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.06e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   94.36
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.79
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.96
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.74
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.21
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.62
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.12
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.54
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.52
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.42
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.51
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.18
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.06
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.52
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10135.78
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.06
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999926564

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.51
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999926993

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    5.95
p-value of test                       :  1.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.82
p-value of test                       :  2.4e-3

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:34.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60588039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5291
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.70
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  175.31
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.97
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45746
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869746
  j =  1                              :        399908510
  j =  2                              :            45742
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45526
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869526
  j =  1                              :        399908952
  j =  2                              :            45518
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.88
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.57
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.41
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.93
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.13
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.35
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.71
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.31
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.57
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.30
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.17
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.18
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12060.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.66
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999996011

Normal statistic for number of bits   :  -0.032
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.97
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000115420

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:37.19

 All tests were passed




Server wird beendet - Lösche Semaphor 61669383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9987


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.76
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7276.62
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.19
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.71
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46276
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870276
  j =  1                              :        399907449
  j =  2                              :            46274
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45582
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869582
  j =  1                              :        399908842
  j =  2                              :            45570
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:11.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.49
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17716.82
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.99
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.63
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.24
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.86
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.98
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.04
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.49
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:17.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.38
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.76
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.12
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10278.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.77
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000046261

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.25
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000072322

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:02:15.44

 All tests were passed




Server wird beendet - Lösche Semaphor 62685191.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4461
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9966

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:11.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.90
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.27
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.04
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908220
  j =  2                              :            45887
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907993
  j =  2                              :            46002
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.5e-3


-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.53
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.72
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.24
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.68
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.69
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.81
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5073.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.09
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.09
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.14
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10257.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.67
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12136.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12154.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.26
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000015658

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.45
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999944486

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:19:38.02

 All tests were passed




Server wird beendet - Lösche Semaphor 42205192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:12.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.74
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.54
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4912.29
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:33.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46546
p-value of test                       :  9.6e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870546
  j =  1                              :        399906909
  j =  2                              :            46544
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908441
  j =  2                              :            45775
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.63e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17042.61
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.38
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.42
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.78
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.23
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.56
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.75
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.24
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.71
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9692.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:33.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.43
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000097693

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.04
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000023707

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:56.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          9.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43024392.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:17.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.73
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4940.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908516
  j =  2                              :            45733
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908045
  j =  2                              :            45970
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.03
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.78e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.70
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.90
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.05
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.96
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.41
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.05
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.82
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.62
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.11
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.35
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.65
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.52
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.85
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:21.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.41
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11561.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.60
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999917408

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.26
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000041056

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:48.20

 All tests were passed




Server wird beendet - Lösche Semaphor 44859400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7166
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:15.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.69
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.51
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7249.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.51
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907796
  j =  2                              :            46102
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908783
  j =  2                              :            45604
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17819.62
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.15
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.49
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.43
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.49
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.28
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.50
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.00
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.54
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.36
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:33.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11601.12
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.65
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999973787

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.81
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000022027

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:52.87

 All tests were passed




Server wird beendet - Lösche Semaphor 45744136.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5269
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:51.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.54
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.69
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.43
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.91
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908050
  j =  2                              :            45966
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908465
  j =  2                              :            45757
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.07e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.58e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.81
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.13
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.67
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.07
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.36
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.80
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.41
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.31
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.61
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.31
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.90
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:33.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.28
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999983384

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999869765

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:10.04

 All tests were passed




Server wird beendet - Lösche Semaphor 47054856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.33
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7295.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.04
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.25
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5068.70
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908373
  j =  2                              :            45806
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907744
  j =  2                              :            46122
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.5e-5    *****

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    8.01
p-value of test                       :  1.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:01.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.74e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.46
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.13
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.21
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.58
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.61
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.58
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.89
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.58
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.05
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.85
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.64
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000020518

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.46
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000072418

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:36.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               1.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48037896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:05:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:05:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:13.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.72
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.92
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.32
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907722
  j =  2                              :            46136
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.94
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.55
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.89
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.76
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.70
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.65
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.54
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.61
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.37
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.54
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  152.52
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10150.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.24
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3916.54
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.41
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999910724

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.28
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000068698

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.10

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:31.37

 All tests were passed




Server wird beendet - Lösche Semaphor 48955400.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9915

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    5.12
p-value of test                       :  2.5e-3

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.78
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.46
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45999
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869999
  j =  1                              :        399908006
  j =  2                              :            45991
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.52e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.58
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17508.97
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.09
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.93
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.56
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.94
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.38
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.75
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.49
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5228.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.32
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.56
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.12
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.68
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.16
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.73
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.51
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11933.47
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.74
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000020341

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.73
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999994343

Normal statistic for number of bits   :  -0.045
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:01.29

 All tests were passed




Server wird beendet - Lösche Semaphor 49938440.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5552
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4180
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.10
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.46
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    3.08
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.58
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.29
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.53
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5196.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908623
  j =  2                              :            45687
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    4.25
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.23
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-3
p-value of test                       :    0.9978

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.51
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.60
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.16
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.58
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.04
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.02
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.17
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.42
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.79
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.45
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.65
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.81
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.40
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.59
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.16
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.16
p-value of test                       :    0.02

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.33e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.90
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5123.14
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.75
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12152.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.52
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999863771

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999999143

Normal statistic for number of bits   : -6.78e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.086
p-value of test                       :    0.47

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:31.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50921480.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.97
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.21
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1485.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.36
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4891.10
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907818
  j =  2                              :            46085
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907960
  j =  2                              :            46020
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:32.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.16
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.34
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:41.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.49
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.50
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.00
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.46
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.95
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.39
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.61
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.34
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.65
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.24
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.2e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5107.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.08
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000031525

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.74
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000128836

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:05.04

 All tests were passed




Server wird beendet - Lösche Semaphor 51806216.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.65
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9958


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45483
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869483
  j =  1                              :        399909041
  j =  2                              :            45469
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908030
  j =  2                              :            45979
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.00e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 7.82e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17614.51
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.99
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.86
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.47
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.80
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.80
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.20
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.02
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.45
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  306.53
p-value of test                       :    0.9971


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.88
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    2.60
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:09.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.92
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000055675

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000007777

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:15.02

 All tests were passed




Server wird beendet - Lösche Semaphor 52723720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7051
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     667
p-value of test                       :  3.8e-3

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   36.37
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.80
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.96
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.92
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.14
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907812
  j =  2                              :            46091
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908389
  j =  2                              :            45798
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.29
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.23
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.57
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.82
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.22
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.26
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.80
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.70
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.35
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.15
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.22
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.50
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10322.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.40
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12140.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.01
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000010150

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   29.70
p-value of test                       :    0.9971


-----------------------------------------------
Total number of bits:  7999941117

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:55.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53772296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5343
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7068
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5090.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:00.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908574
  j =  2                              :            45704
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908624
  j =  2                              :            45685
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.83
p-value of test                       :  3.6e-3

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.85
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.25
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.71
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.49
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.00
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.62
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.17
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.24
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.45
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.57
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -2.48
p-value of test                       :    0.9934



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.00
p-value of test                       :  7.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 3.67e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:11.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.62
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.65
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000029242

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.56
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999831947

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:58.42

 All tests were passed




Server wird beendet - Lösche Semaphor 54820872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9946

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.19
p-value of test                       :  7.2e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6746.65
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.25
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.95
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908225
  j =  2                              :            45883
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908224
  j =  2                              :            45879
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.86e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.13
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.27
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.15
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.44
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.72
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.30
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.48
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.30
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.31
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5020.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.78
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999944396

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000063151

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.086
p-value of test                       :    0.47

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.11

 All tests were passed




Server wird beendet - Lösche Semaphor 55902216.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.28
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.91
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908275
  j =  2                              :            45861
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45793
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869793
  j =  1                              :        399908415
  j =  2                              :            45791
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.37e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.75
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17653.97
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.39
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.26
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.77
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4761.94
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.04
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    2.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.73
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.83
p-value of test                       :  5.2e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.031
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.75
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999797780

Normal statistic for number of bits   :   -1.60
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.16
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000098686

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:24.70

 All tests were passed




Server wird beendet - Lösche Semaphor 56918024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5224
p-value of test                       :    0.9964


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4203
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    3.16
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     652
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.73
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   89.19
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.32
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.51
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.23
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.01
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908372
  j =  2                              :            45805
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907814
  j =  2                              :            46087
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.56
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.61
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.92
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.95
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.32
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.55
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.73
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.53
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.28
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.69
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.06
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.65
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999896879

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.24
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000066526

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:44.34

 All tests were passed




Server wird beendet - Lösche Semaphor 58097672.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.78
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.62
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1574.53
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.55
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.83
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.76
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5312.22
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:55.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908874
  j =  2                              :            45560
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908578
  j =  2                              :            45708
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-6
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    : 3.80e-4
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.96
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.42
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.90
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.42
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.03
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.88
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.65
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.87
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.57
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.17
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.88
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.01
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.57
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4702.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:32.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.16
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999865289

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.16
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000058534

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:11.20

 All tests were passed




Server wird beendet - Lösche Semaphor 59146248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    3.38
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.35
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.63
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.81
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.22
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46091
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870091
  j =  1                              :        399907821
  j =  2                              :            46085
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908634
  j =  2                              :            45680
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17204.84
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.48
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.44
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.06
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.34
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.97
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.24
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.04
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.67
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.23
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.69
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.46
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.34
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.83
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000094267

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.38
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000119968

Normal statistic for number of bits   :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    2.41
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:51.85

 All tests were passed




Server wird beendet - Lösche Semaphor 60194824.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5342
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.14
p-value of test                       :    0.9994    *****

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9964

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1505.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.28
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907848
  j =  2                              :            46073
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908075
  j =  2                              :            45955
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.91e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.99e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17136.00
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.44
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.17
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.00
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.26
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.70
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.55
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.15
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.37
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.75
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.42e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.55
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  256.43
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.43
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000072646

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.11
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000027790

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61145096.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.83
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:59.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908380
  j =  2                              :            45804
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907899
  j =  2                              :            46049
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.85e-4
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17118.35
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.92
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.29
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.62
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.00
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.69
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.86
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  559.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.18
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.51
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.36
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.89
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.81
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.65
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.21
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.17
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.19
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9775.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:15.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5117.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.77
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.32
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000160492

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.18
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999927890

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:59.76

 All tests were passed




Server wird beendet - Lösche Semaphor 62193672.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:05:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:05:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.68
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     656
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.59
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.60
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.89
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45591
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869591
  j =  1                              :        399908821
  j =  2                              :            45585
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908487
  j =  2                              :            45752
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:32.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-4
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 3.20e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.69
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.28
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.39
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.80
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.15
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.90
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5267.54
p-value of test                       :  4.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.93
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.67
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.86e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.38
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.07
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000005821

Normal statistic for number of bits   :   0.046
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.95
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999852353

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9945

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.53

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:26:47.34

 All tests were passed




Server wird beendet - Lösche Semaphor 42237961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5359
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:11.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.33
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.85
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.75
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7236.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.41
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.22
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907841
  j =  2                              :            46075
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908578
  j =  2                              :            45708
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.61
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17220.39
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.39
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.10
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.00
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.72
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4795.85
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.44
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.68
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.59
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.81
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.69
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:20.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.61
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.62
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.46
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000098281

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.95
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999914654

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    2.51
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:07.32

 All tests were passed




Server wird beendet - Lösche Semaphor 43352073.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.80
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.87
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.25
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.52
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908528
  j =  2                              :            45727
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908755
  j =  2                              :            45618
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.05e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-5
p-value of test                       :    0.9947

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.49
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.73
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17138.61
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.93
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.20
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.15
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.85
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.74
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.60
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.33
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.94
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.86
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.48
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -2.34
p-value of test                       :    0.9904



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.86
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000165418

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.92
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999946244

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:01.85

 All tests were passed




Server wird beendet - Lösche Semaphor 44466185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997261
  j =  2                              :             1368
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  364.44
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.25
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.07
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907841
  j =  2                              :            46072
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908589
  j =  2                              :            45701
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17306.17
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.68
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.91
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.00
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.77
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.69
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.27
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.38
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.12
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  318.19
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.56
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.66
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.23
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.08
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 7.98e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.44
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:33.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.14
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.16
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999971111

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.70
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999961283

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:32.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 R (L=50, r=0)       0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45350921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.24
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.22
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.67
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907898
  j =  2                              :            46042
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908330
  j =  2                              :            45826
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.34e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17773.23
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.51
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.86
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.79
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.75
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  469.09
p-value of test                       :  1.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.42
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.17
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.37
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.56
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.15
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.23
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.42
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-4
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 9.02e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.26
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4741.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.15
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999818459

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.30
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000137773

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:07.21

 All tests were passed




Server wird beendet - Lösche Semaphor 46563337.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.12
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.14
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.00
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4813.90
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907862
  j =  2                              :            46066
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.43
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17332.22
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.57
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.78
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.39
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.87
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.98
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.90
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.70
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.69
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.00
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.15
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9934

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:42.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.88
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.57
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000036286

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.84
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000089221

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9944

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:51.01

 All tests were passed




Server wird beendet - Lösche Semaphor 47579145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1485
p-value of test                       :  6.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334605
  j =  1                              :        599997030
  j =  2                              :             1485
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.64
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.71
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908205
  j =  2                              :            45887
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908308
  j =  2                              :            45840
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.63e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17443.64
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.21
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.42
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.91
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5149.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.11
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.06
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.21
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.11
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.74
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.77
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.16
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000124504

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.20
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000076126

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.89
p-value of test                       :  2.0e-3

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:57.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            6.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48988169.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4205
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.86
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.96
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.24
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.96
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45973
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869973
  j =  1                              :        399908059
  j =  2                              :            45963
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45895
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869895
  j =  1                              :        399908214
  j =  2                              :            45887
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    3.96
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.14e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.64
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   32.41
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.43
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.68
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.80
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.39
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.63
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  140.77
p-value of test                       :  4.7e-6    *****


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.42
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.58
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.45
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.91
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.34
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.82e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.71
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999906371

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.34
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999841244

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.090
p-value of test                       :    0.46

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9999 
 77  RandomWalk1 C (L=1000, r=20)    4.7e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49905673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:40.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5538
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.62
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.04
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.29
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.97
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:10.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.39
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.64
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:07.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908349
  j =  2                              :            45815
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45436
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869436
  j =  1                              :        399909129
  j =  2                              :            45434
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.96
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.78
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.13
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.48
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.43
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.76
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.61
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5154.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.55
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.24
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.63
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.95
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.05
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.36
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.95
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:04:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.47
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.4e-3

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5125.05
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.58
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000095035

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.85
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000107509

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:15.57

 All tests were passed




Server wird beendet - Lösche Semaphor 50888713.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     966
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:41.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.33
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  510.44
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.18
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:10.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908552
  j =  2                              :            45718
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45606
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869606
  j =  1                              :        399908790
  j =  2                              :            45602
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.03
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.52
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17589.65
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  198.69
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.26
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.45
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.32
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.58
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.51
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.12
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5133.62
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.59
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.64
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.54
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.68
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    2.28
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.13
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.95
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.35
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12148.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.66
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000074023

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.83
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999975851

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:11.32

 All tests were passed




Server wird beendet - Lösche Semaphor 51838985.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997401
  j =  2                              :             1298
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7092
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:02.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.12
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7144.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.25
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.12
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.83
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.12
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908332
  j =  2                              :            45828
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908216
  j =  2                              :            45892
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.64
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.04
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.87
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.64
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.56
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.42
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.84
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.27
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.62
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.14e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.27
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4761.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4270.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11953.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.04
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000036541

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.17
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000099193

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  9.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.65
p-value of test                       :  4.0e-3

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:30.20

 All tests were passed




Server wird beendet - Lösche Semaphor 52822025.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.15
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.42
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.71
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907852
  j =  2                              :            46065
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908364
  j =  2                              :            45809
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   35.60
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.35
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.62
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.97
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.77
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.65
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.86
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5283.64
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.25
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.89
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.87e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.06
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.01
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.02
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12095.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.68
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999965234

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.07
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999952424

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.066
p-value of test                       :    0.47

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:19.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 60  WeightDistrib, r = 20           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54001673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1579.18
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.08
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.18
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46167
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870167
  j =  1                              :        399907675
  j =  2                              :            46149
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908683
  j =  2                              :            45648
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  4.9e-4    *****

Anderson-Darling statistic = A2       :    4.93
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.78
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.22
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.59
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.30
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.12
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.32
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.73
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.11
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.81
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.50
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:16.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5026.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.01
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000043828

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.14
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000100108

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:54.57

 All tests were passed




Server wird beendet - Lösche Semaphor 55017481.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    4.23
p-value of test                       :  6.8e-3

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7029.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908028
  j =  2                              :            45983
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907547
  j =  2                              :            46222
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17373.73
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.41
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.85
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.39
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.63
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.40
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.34
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:28.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.16
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.55
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.73
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999922589

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.68
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000010195

Normal statistic for number of bits   :   0.081
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:20.19

 All tests were passed




Server wird beendet - Lösche Semaphor 56033289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:13.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.11
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.76
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45788
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869788
  j =  1                              :        399908430
  j =  2                              :            45776
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908042
  j =  2                              :            45976
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:33.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.61e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17421.40
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.45
p-value of test                       :    0.9976


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.33
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.65
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5227.24
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.39
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.97
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.60
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.31
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5025.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11553.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.53
p-value of test                       :    0.9909


-----------------------------------------------
Total number of bits:  8000039154

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.51
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000049771

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:54.47

 All tests were passed




Server wird beendet - Lösche Semaphor 57081865.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.80
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.43
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.04
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.07
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4804.91
p-value of test                       :    0.9909


-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908180
  j =  2                              :            45901
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908133
  j =  2                              :            45929
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.98e-3
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.80
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.14e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   89.62
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17548.80
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.02
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.25
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.90
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.89
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.05
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.01
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.07
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.96e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   46.00
p-value of test                       :  7.1e-5    *****



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.51
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.17
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999946634

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.72
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999892043

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :  -0.069
p-value of test                       :    0.53

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         : -8.62e-3
p-value of test                       :    0.50

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:48.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 86  LongestHeadRun, r = 0           7.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58228745.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7142
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    4.16
p-value of test                       :  7.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     817
p-value of test                       :    0.9973

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9913

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6867.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.65
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.39
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907709
  j =  2                              :            46141
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46263
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870263
  j =  1                              :        399907476
  j =  2                              :            46259
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:32.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.62e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -3.16
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.08
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.94
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.64
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.39
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.95
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.96
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.62
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.51
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.43
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5153.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.88
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.75
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.41
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9922

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.48e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   26.17
p-value of test                       :  9.8e-4    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.68
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3918.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.65
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000065086

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.11
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000002464

Normal statistic for number of bits   :   0.019
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:17.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 56  SampleCorr, k = 2               0.9992 
 86  LongestHeadRun, r = 0           9.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59342857.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    4.09
p-value of test                       :  7.9e-3

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.58
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:54.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907919
  j =  2                              :            46039
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908608
  j =  2                              :            45690
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.99e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.33
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.34
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.95
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.48
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.09
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.61
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.63
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.65
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.48
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.15
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.31
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.59
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.09
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5236.25
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.44
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:20.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:33.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.70
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999863189

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.18
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999951500

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:19.61

 All tests were passed




Server wird beendet - Lösche Semaphor 60358665.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    2.78
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    3.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.41
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908697
  j =  2                              :            45650
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908745
  j =  2                              :            45626
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.23
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.78
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17056.76
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.93
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.88
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.60
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.11
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.53
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.50
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.49
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.18
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.90
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.87
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999864860

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.64
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000055762

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:13.62

 All tests were passed




Server wird beendet - Lösche Semaphor 61603849.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4198
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.26
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.35
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5212.31
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908508
  j =  2                              :            45743
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.52
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.52
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.34
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.32
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.84
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.03
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.87
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.39
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.42
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.30
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.34
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.58
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999948707

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.69
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999909917

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:03:00.85

 All tests were passed




Server wird beendet - Lösche Semaphor 62554121.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    3.23
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    4.15
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.48
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.71
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.20
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.46
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:24.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908433
  j =  2                              :            45779
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908399
  j =  2                              :            45796
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:33.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-4    *****

Anderson-Darling statistic = A2       :    6.84
p-value of test                       :  4.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  8.9e-5    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17330.33
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.24
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.20
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.67
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.41
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.33
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.18
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.86
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.04
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.12
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.54
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:33.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.82
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.26
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.94
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.93
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11725.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.08
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999976163

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.06
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999982790

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         : -2.68e-3
p-value of test                       :    0.50

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:52.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           1.5e-4
 47  MaxOft, t = 16                  8.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42270730.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6767.96
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.34
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.47
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:17.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908748
  j =  2                              :            45620
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908029
  j =  2                              :            45978
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.85
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17128.86
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.07
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.86
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.03
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.62
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.41
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:33.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.92
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:34.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.05
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.12
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.37
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9803.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -5.58e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.37
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   88.15
p-value of test                       :  2.3e-3


-----------------------------------------------
Total number of bits:  7999824357

Normal statistic for number of bits   :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.08
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000007285

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    2.58
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.9918

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:19.44

 All tests were passed




Server wird beendet - Lösche Semaphor 43679754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5564
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.45
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.55
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.83
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.09
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.84
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908802
  j =  2                              :            45593
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907949
  j =  2                              :            46021
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.70e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.07
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.66
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.62
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.88
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.44
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.55
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.07
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.96
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.60
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.04
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.63
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.94
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.16
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.08
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.50
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000072976

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.82
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999944441

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:01.85

 All tests were passed




Server wird beendet - Lösche Semaphor 44531722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7505
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.89
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.24
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:47.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.37
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4832.74
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:23.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908245
  j =  2                              :            45876
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.5e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.63e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17451.93
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.71
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.53
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.52
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.69
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.31
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.90
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4884.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.66
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.35
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.29
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.11
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.81
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4345.36
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.98
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000049855

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.40
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999958973

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:17:10.95

 All tests were passed




Server wird beendet - Lösche Semaphor 45416458.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5534
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.13
p-value of test                       :  2.8e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.76
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.58
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908190
  j =  2                              :            45902
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45687
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869687
  j =  1                              :        399908630
  j =  2                              :            45679
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-5
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    : 2.97e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   70.99
p-value of test                       :  6.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.9922

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17008.74
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.28
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.15
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.19
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.17
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.84
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.44
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.69
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.04
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.02
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.60
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.57
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.08
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.37
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.65
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.14
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.80e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    5.12
p-value of test                       :  2.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9549.24
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.72
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.94
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:33.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.67
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999985955

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.81
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000065038

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:18.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 63  WeightDistrib, r = 10           6.5e-4
 90  HammingWeight2, r = 0           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46858250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9954

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.69
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7178.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.72
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907771
  j =  2                              :            46110
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.80e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.18e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.23
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.89
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.42
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.13
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.15
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.01
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  435.74
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.87
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.11
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.71
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4794.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.99
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000006268

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.88
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999936311

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.9999    *****

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.1e-3

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.59
p-value of test                       :  4.8e-3

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:59.65

 All tests were passed




Server wird beendet - Lösche Semaphor 47808522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.20
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.48
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.04
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.13
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.47
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.99
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7274.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.00
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.82
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908398
  j =  2                              :            45798
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907734
  j =  2                              :            46130
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.62
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17546.37
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.97
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.65
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.59
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.25
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.38
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.06
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.49
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.86
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.12
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.99
p-value of test                       :    0.9926


-----------------------------------------------
Total number of bits:  7999897938

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.95
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000097501

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.06
p-value of test                       :    0.98

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:14.17

 All tests were passed




Server wird beendet - Lösche Semaphor 48726026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997287
  j =  2                              :             1355
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4469
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.17
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.06
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.84
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908557
  j =  2                              :            45720
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908295
  j =  2                              :            45845
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :  2.4e-4    *****

Anderson-Darling statistic = A2       :    5.33
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17791.69
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.67
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.92
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.10
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.66
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4808.07
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.43
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.76
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:33.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4735.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4636.58
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.47
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.22
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.41
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.10
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999956711

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.48
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000009427

Normal statistic for number of bits   :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:03.29

 All tests were passed




Server wird beendet - Lösche Semaphor 49676298.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7074
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9920

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9916

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.49
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.01
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.26
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.79
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908341
  j =  2                              :            45822
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908488
  j =  2                              :            45753
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.11
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.44
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.57
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17179.62
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.23
p-value of test                       :    0.9970


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.79
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.48
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.41
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.15
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4837.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.65
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.68
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.67
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.59e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.95
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:13.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.76
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4745.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.77
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.37
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000069985

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.92
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999980966

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.22
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:48.05

 All tests were passed




Server wird beendet - Lösche Semaphor 50954250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.51
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.76
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.84
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.28
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.14
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907881
  j =  2                              :            46046
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908250
  j =  2                              :            45869
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.83e-6
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.74
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.96
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.76
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.34
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.44
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.63
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.24
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.60
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.95
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.50
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.25e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.80e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.61
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.51
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12056.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000029980

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.25
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999959555

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:34.54

 All tests were passed




Server wird beendet - Lösche Semaphor 51871754.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    3.73
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.16
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6776.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.84
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.62
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.50
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45617
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869617
  j =  1                              :        399908773
  j =  2                              :            45603
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907911
  j =  2                              :            46037
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.52e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17460.71
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.27
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.02
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.18
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.18
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.93
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.72
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.70
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.13
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.55
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.34e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.16
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.18
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000022048

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.58
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000031414

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:13.02

 All tests were passed




Server wird beendet - Lösche Semaphor 52789258.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  168.51
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.47
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.78
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.67
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908586
  j =  2                              :            45701
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45489
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869489
  j =  1                              :        399909026
  j =  2                              :            45481
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    5.76
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.61e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.17e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.96
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.06
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.28
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.96
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.17
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.79
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.30
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.81
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.43
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.93
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.03
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.80
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.32
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.81e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.97
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.51
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12094.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.41
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999931442

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.69
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000129793

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:35.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      0.9994 
 46  MaxOft, t = 8                   6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53870602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.84
p-value of test                       :  3.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    2.01
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.66
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.91
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  177.07
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1560.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7229.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.15
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.01
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5233.43
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908150
  j =  2                              :            45919
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45863
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869863
  j =  1                              :        399908276
  j =  2                              :            45859
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.93e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.39
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.29
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17189.42
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.11
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.29
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.31
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.14
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.47
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.80
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.54
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.85
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.13
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.29
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 4.79e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.81
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.10
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10114.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.08
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.91
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999951698

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.93
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000095968

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:15.97

 All tests were passed




Server wird beendet - Lösche Semaphor 54886410.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5563
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:40.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7574
p-value of test                       :  1.5e-3


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.43
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.97
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908339
  j =  2                              :            45829
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908252
  j =  2                              :            45868
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9920


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.34e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17576.98
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.17
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.88
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.82
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.97
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.35
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  468.46
p-value of test                       :  1.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.84
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.11
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.28
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -2.25
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.34
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.21
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3946.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.91
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999989042

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.03
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999974375

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Tests on the sum of all N observations
Standardized normal statistic         : -2.44e-3
p-value of test                       :    0.50

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:12.85

 All tests were passed




Server wird beendet - Lösche Semaphor 55934986.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5291
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9981

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.88
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.17
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.02
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907720
  j =  2                              :            46137
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45798
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869798
  j =  1                              :        399908407
  j =  2                              :            45792
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.60e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.47
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.25
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.96
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   87.60
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.24
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.80
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.44
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  161.63
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.42
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.68
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.01
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9965

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.66
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.9945

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.53
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999889571

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.43
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000066730

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.53

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:19.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56950794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5536
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.86
p-value of test                       :  3.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.81
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.08
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.83
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.27
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:56.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46354
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870354
  j =  1                              :        399907294
  j =  2                              :            46350
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907957
  j =  2                              :            46020
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.00e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.01
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.26
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.34
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17110.63
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.85
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.31
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.86
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.00
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.98
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.05
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.80
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.54
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.83e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.81
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:20.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.27
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.56
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999937820

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.09
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999990854

Normal statistic for number of bits   :  -0.072
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.042
p-value of test                       :    0.48

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:01.30

 All tests were passed




Server wird beendet - Lösche Semaphor 57966602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7130
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.22
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     179
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.81
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.80
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.43
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:54.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907746
  j =  2                              :            46124
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45969
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869969
  j =  1                              :        399908065
  j =  2                              :            45963
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.77e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.98
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.26
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.59
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.63
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.22
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.95
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.74
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.87
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.11
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.85
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.93
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.75
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.68
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9789.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.37
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.90
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000175675

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999983435

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.57
p-value of test                       :  5.1e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.04

 All tests were passed




Server wird beendet - Lösche Semaphor 58982410.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1241
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334361
  j =  1                              :        599997518
  j =  2                              :             1241
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4178
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    2.55
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  511.60
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.60
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6933.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.86
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.54
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  6.5e-3


-----------------------------------------------
CPU time used                    :  00:02:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907736
  j =  2                              :            46126
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908601
  j =  2                              :            45689
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.22
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.89
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17371.78
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.85
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.22
p-value of test                       :    0.9996    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.35
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.00
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.29
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.25
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.05
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.71
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.44
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.10
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.42
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.15
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.87
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.49
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.56
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.82
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.36
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999947753

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000206362

Normal statistic for number of bits   :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.09
p-value of test                       :    0.98

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.92
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            0.9996 
 75  RandomWalk1 R (L=50, r=25)      0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59998218.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.76
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:51.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.28
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.27
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7276.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.98
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.61
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:01.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908350
  j =  2                              :            45822
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908423
  j =  2                              :            45784
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.89e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.09
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17319.19
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.29
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.61
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.58
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.56
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.53
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.83
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.36
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.86
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.25
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.23
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.91
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.73
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.79
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.55
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.07
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.19
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:16.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.68
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000080419

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.29
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999921155

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:55.12

 All tests were passed




Server wird beendet - Lösche Semaphor 61046794.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.68
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.71
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:20.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.09
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5182.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45741
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869741
  j =  1                              :        399908521
  j =  2                              :            45735
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46124
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870124
  j =  1                              :        399907758
  j =  2                              :            46112
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.32e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.88e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.73
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.33
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.44
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.18
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.09
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.42
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5156.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.57
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.87
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.57
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.97e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.72
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.84
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11561.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.63
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999998141

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.38
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999944474

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9912

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:09.70

 All tests were passed




Server wird beendet - Lösche Semaphor 62095370.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1205
p-value of test                       : 1 -  5.9e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334325
  j =  1                              :        599997590
  j =  2                              :             1205
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    3.94
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.74
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5227.37
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908136
  j =  2                              :            45920
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908317
  j =  2                              :            45831
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.1e-3

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.35
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.92
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.28
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.77
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.12
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    2.32
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.48
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.44
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10237.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:22.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.92
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.20
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000150421

Normal statistic for number of bits   :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.79
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999853580

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:22.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  5.9e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42303499.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    2.28
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.66
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.83
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.51
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5180.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907819
  j =  2                              :            46083
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908410
  j =  2                              :            45789
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9974


-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.6e-3


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 6.60e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.22
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.41
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.06
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.30
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.18
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5139.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.01
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.72
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.84
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.22
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -2.20
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.50
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9746.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.12
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999912269

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.83
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000056386

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:47.01

 All tests were passed




Server wird beendet - Lösche Semaphor 43450379.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7533
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.05
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:41.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1387.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6861.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:32.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.73
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5014.60
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46219
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870219
  j =  1                              :        399907567
  j =  2                              :            46209
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46268
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870268
  j =  1                              :        399907470
  j =  2                              :            46256
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.10e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.23e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.11
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.77
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.53
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.25
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.27
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.07
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.86
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.99
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.20
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.95
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.93
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.99
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.23
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.62
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000012946

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.36
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999944414

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:35.06

 All tests were passed




Server wird beendet - Lösche Semaphor 44171275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    3.17
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6924.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.25
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.22
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907551
  j =  2                              :            46214
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908344
  j =  2                              :            45828
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.38e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.45
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17550.17
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.87
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.84
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.77
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.96
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.87
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.44
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.66
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.67
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.45
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.06
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.47
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.63e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.51
p-value of test                       :    0.9925

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10277.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5030.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11525.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12042.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.32
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999829907

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.96
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999986111

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.97

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:48.38

 All tests were passed




Server wird beendet - Lösche Semaphor 45318155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    3.21
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     832
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.00
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4849.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908762
  j =  2                              :            45610
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46251
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870251
  j =  1                              :        399907498
  j =  2                              :            46251
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.29e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.39
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17680.96
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.26
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.95
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.02
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  306.70
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.94
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.76
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.04
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.87
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.84
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999812387

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.40
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000104230

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:06.05

 All tests were passed




Server wird beendet - Lösche Semaphor 46399499.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7471
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    4.17
p-value of test                       :  7.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:12.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.28
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.27
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5035.59
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:58.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908638
  j =  2                              :            45678
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908661
  j =  2                              :            45662
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:31.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.65e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17231.14
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.07
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.53
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.19
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.26
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.45e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.34
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.07
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.47
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11517.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11672.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.69
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999907502

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.30
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000053296

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:42.68

 All tests were passed




Server wird beendet - Lösche Semaphor 47415307.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5532
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   91.42
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.88
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.36
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.84
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:56.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46201
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870201
  j =  1                              :        399907601
  j =  2                              :            46195
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908348
  j =  2                              :            45823
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.42e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.25
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.46
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.38
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.35
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.60
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.45
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.99
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.06
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.63
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.96
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.36
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.98
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    6.06
p-value of test                       :  9.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  154.80
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9907.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4791.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.21
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000105376

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.71
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000158053

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.50
p-value of test                       :    0.9937

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:21.12

 All tests were passed




Server wird beendet - Lösche Semaphor 48463883.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.83
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   24.27
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.11
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1323.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6774.66
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.72
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.65
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:56.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908182
  j =  2                              :            45903
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46421
p-value of test                       :  5.8e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870421
  j =  1                              :        399907165
  j =  2                              :            46407
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-4
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    : 6.84e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.03
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.56
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.32
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.12
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.76
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.55
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.26
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.56
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  256.02
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.44
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.1e-3

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10352.02
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.42
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9609.97
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4934.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.55
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3959.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11454.79
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.20
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999996041

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.22
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999947066

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:44.32

 All tests were passed




Server wird beendet - Lösche Semaphor 49479691.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1454
p-value of test                       :  8.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334574
  j =  1                              :        599997092
  j =  2                              :             1454
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.59
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.81
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.89
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.08
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908167
  j =  2                              :            45912
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908481
  j =  2                              :            45752
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.39e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 3.04e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.78
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17386.70
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.82
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.97
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.09
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.53
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.69
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.19
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.99
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.93
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.28
p-value of test                       :    0.01

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.81
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.44
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999874004

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.92
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999935690

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.58
p-value of test                       :  4.9e-3

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:50.01

 All tests were passed




Server wird beendet - Lösche Semaphor 50692107.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4472
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.15
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.40
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.73
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:54.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908592
  j =  2                              :            45695
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907972
  j =  2                              :            46005
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.62e-4
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17158.95
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.73
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.18
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.65
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.67
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5219.52
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.60
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.26
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.91
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    5.51
p-value of test                       :  1.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.03
p-value of test                       :  1.2e-3

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.95e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.61
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5105.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.14
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.91
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.22
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999989954

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.21
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000132103

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.71

 All tests were passed




Server wird beendet - Lösche Semaphor 51675147.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.10
p-value of test                       :  8.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.56
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.19
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.26
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.68
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908008
  j =  2                              :            45993
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908223
  j =  2                              :            45887
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-6
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    : 2.82e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.14
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.16
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.83
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.90
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.94
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.96
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.04
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.38
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.13
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.63
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.11
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.59
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.03
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.27
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9769.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5105.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.43
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.41
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000267445

Normal statistic for number of bits   :    2.11
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.95
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999999713

Normal statistic for number of bits   : -2.27e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    2.58
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:29.78

 All tests were passed




Server wird beendet - Lösche Semaphor 52658187.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7530
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:04:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.16
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45336
p-value of test                       :    0.9944


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869336
  j =  1                              :        399909331
  j =  2                              :            45330
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908102
  j =  2                              :            45940
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.19e-3
p-value of test                       :    0.9943

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.31e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17290.37
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.02
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.18
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.26
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.73
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.52
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.49
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.47
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.40
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.89
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.50
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.81
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.58
p-value of test                       :    0.94

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.82
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.63
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:20.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.69
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999896972

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.17
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999957626

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.17

 All tests were passed




Server wird beendet - Lösche Semaphor 53641227.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.75
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.54
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.25
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4881.92
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:59.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907812
  j =  2                              :            46085
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:29.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    : 1.06e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.61e-4
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17787.11
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.98
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.56
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.66
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.86
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.83
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.01
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:34.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.76
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.78
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.09
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.64
p-value of test                       :    0.9959

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.29
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.72
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.83
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.11
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000089665

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.94
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999928574

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         : 8.86e-3
p-value of test                       :    0.50

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.18
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.46

 All tests were passed




Server wird beendet - Lösche Semaphor 54689803.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6729.53
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5140.39
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907859
  j =  2                              :            46066
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907816
  j =  2                              :            46089
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.52e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17156.18
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.10
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.84
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.68
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.87
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.63
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.23
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.34
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.93
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999963086

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.91
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999994154

Normal statistic for number of bits   :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:39.37

 All tests were passed




Server wird beendet - Lösche Semaphor 55705611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7524
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.09
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.75
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.46
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.41
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908050
  j =  2                              :            45966
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46267
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870267
  j =  1                              :        399907468
  j =  2                              :            46263
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:29.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.43e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.65e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -2.80e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    5.58
p-value of test                       :  1.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  191.33
p-value of test                       :  3.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17593.52
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.80
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.20
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.00
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.93
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.57
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.63
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.25
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.17
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.89
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.83
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.94
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.80
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.68
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.08
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000143866

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.55
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000123208

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         : 9.44e-3
p-value of test                       :    0.50

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.3e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    5.14
p-value of test                       :  2.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.45
p-value of test                       :    0.9928

Sample variance                       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 72  Savir2                          3.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56786955.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.89
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    6.25
p-value of test                       :  7.6e-4    *****

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.84
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.45
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4874.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908500
  j =  2                              :            45744
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.79
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.05
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17479.11
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.30
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.01
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.05
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.40
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.32
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.47
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.30
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.68
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.43
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10164.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10254.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5098.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.46
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.82
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999900608

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.39
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000110845

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3          7.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57802763.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7049.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.46
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.07
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45433
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869433
  j =  1                              :        399909141
  j =  2                              :            45419
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908591
  j =  2                              :            45694
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.78e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.84e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.02
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.78
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.39
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.92
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.57
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.00
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.66
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.79
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.22
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.35
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.55
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.11e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.52
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10368.34
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.42
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.09
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.19
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999911093

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000087073

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:34.23

 All tests were passed




Server wird beendet - Lösche Semaphor 58818571.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.49
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  377.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:21.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.41
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907887
  j =  2                              :            46049
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907703
  j =  2                              :            46144
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.92e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.13
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.68
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.50
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.62
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.28
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.67
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.00
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.44
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.20
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.42
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.88
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.88
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.85
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999843572

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   97.13
p-value of test                       :  2.9e-4    *****


-----------------------------------------------
Total number of bits:  8000065950

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:57.59
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             2.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59834379.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4171
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.60
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.41
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.58
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.60
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45322
p-value of test                       :    0.9954


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869322
  j =  1                              :        399909363
  j =  2                              :            45308
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45317
p-value of test                       :    0.9957


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869317
  j =  1                              :        399909369
  j =  2                              :            45311
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.71
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.65
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17477.36
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.10
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.83
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.96
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.52
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.60
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.35
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.23
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.40
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.15e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.29
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    5.67
p-value of test                       :  1.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4590.51
p-value of test                       :    0.9990

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3906.01
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.21
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999966746

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.60
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000100117

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:09.23

 All tests were passed




Server wird beendet - Lösche Semaphor 60948491.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:46.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9977


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.68
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6830.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5289.62
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46333
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870333
  j =  1                              :        399907337
  j =  2                              :            46327
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908501
  j =  2                              :            45739
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    4.89
p-value of test                       :  3.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.73
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17545.44
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.92
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.71
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   48.09
p-value of test                       :  8.3e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  589.57
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.10
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.54
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.06
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.73
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:14.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12068.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.77
p-value of test                       :  3.8e-3


-----------------------------------------------
Total number of bits:  8000337180

Normal statistic for number of bits   :    2.67
p-value of test                       :  3.8e-3



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.23
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999994040

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    3.26
p-value of test                       :  5.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:29.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 C (L=50, r=25)      8.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61964299.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997271
  j =  2                              :             1363
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.88
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.67
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908062
  j =  2                              :            45966
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908467
  j =  2                              :            45759
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:34.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.04e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.30
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.06
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.82
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.88
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.20
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.18
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:47.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.82
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.93
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.47
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.93
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.05
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.09
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000050827

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.21
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999984743

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:33.29

 All tests were passed




Server wird beendet - Lösche Semaphor 42336268.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9923

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.43
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.23
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.29
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  8.8e-3

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.32
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907927
  j =  2                              :            46035
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45451
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869451
  j =  1                              :        399909101
  j =  2                              :            45445
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:33.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.73
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.15
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.33
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.28
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.36
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  429.94
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.27
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.70
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.71
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.86
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.91
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.41
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.13
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000055462

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.33
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999996002

Normal statistic for number of bits   :  -0.032
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:07.92

 All tests were passed




Server wird beendet - Lösche Semaphor 43483148.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.57
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    5.87
p-value of test                       :  1.1e-3

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.53
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.00
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.02
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.90
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.58
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908293
  j =  2                              :            45843
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908678
  j =  2                              :            45655
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:34.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.50
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.90
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.51
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.97
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.54
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.42
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.99
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.23
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.62
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.56
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.04
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.04
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.69
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.35
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.40
p-value of test                       :  8.2e-3

Sample variance                       :    0.21
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.64e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.37
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.67
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.26
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.87
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000109663

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.71
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000014680

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:49.35

 All tests were passed




Server wird beendet - Lösche Semaphor 44302348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:47.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.21
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.28
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.61
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.85
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.66
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46125
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870125
  j =  1                              :        399907751
  j =  2                              :            46123
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907594
  j =  2                              :            46191
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17704.75
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.97
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.45
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.34
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.68
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.72
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.57
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  461.93
p-value of test                       :  2.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.48
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.24
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.19
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.47
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.93
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.18
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4298.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11657.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.89
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000032875

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.54
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000027166

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.22
p-value of test                       :    0.01

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:53.05

 All tests were passed




Server wird beendet - Lösche Semaphor 45285388.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.44
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.60
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:22.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:00.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46159
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870159
  j =  1                              :        399907687
  j =  2                              :            46149
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908258
  j =  2                              :            45865
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  108.27
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.87
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.17
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.07
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.60
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.90
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.51
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5203.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.79
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.53
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.47
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.03
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.56
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.11
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10319.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.68
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:34.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.43
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999916160

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.50
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000007267

Normal statistic for number of bits   :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.30e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.91
p-value of test                       :  1.8e-3

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.017
p-value of test                       :    0.49

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:19.57

 All tests were passed




Server wird beendet - Lösche Semaphor 46301196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5302
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4213
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.21
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    3.65
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.57
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.60
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45478
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869478
  j =  1                              :        399909049
  j =  2                              :            45468
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908513
  j =  2                              :            45733
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:33.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.49e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.41
p-value of test                       :  3.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.49
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.02
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.12
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.63
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.31
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.34
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.42
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.98
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.55
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.73
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5227.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.25
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.67e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.11
p-value of test                       :  9.9e-3

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.61
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000027025

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.94
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999934859

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:32.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 58  AppearanceSpacings, r = 27      3.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47513612.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5603
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.46
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5289.53
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908156
  j =  2                              :            45913
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908172
  j =  2                              :            45908
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-6
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.042
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.41
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.11
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.90
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.90
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.48
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.83
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.68
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.56
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.65
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.26
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.05
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.74
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.82
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.082
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:34.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.34
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999893585

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.27
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999866354

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:05.28

 All tests were passed




Server wird beendet - Lösche Semaphor 48627724.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.17
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    7.34
p-value of test                       :  2.4e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.58
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.02
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  161.10
p-value of test                       :  6.2e-3


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.66
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:54.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908009
  j =  2                              :            45994
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908493
  j =  2                              :            45749
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:19.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.58
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   69.39
p-value of test                       :  9.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.04e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17482.58
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.18
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.04
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.01
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    2.39
p-value of test                       :  8.5e-3



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.49
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.17e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.35
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.91
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.87
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4248.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.66
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999900650

Normal statistic for number of bits   :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.29
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000111253

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:28.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         2.4e-4
 63  WeightDistrib, r = 10           9.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50200588.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.41

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.38
p-value of test                       :  6.7e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.46
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.33
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.55
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.39
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907857
  j =  2                              :            46064
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45570
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869570
  j =  1                              :        399908863
  j =  2                              :            45564
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:29.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17553.74
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.91
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.99
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.28
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.07
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.89
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.28
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.18
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.08
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.32
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.18
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.75
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:15.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.91
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.65
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000099337

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.56
p-value of test                       :  6.1e-3


-----------------------------------------------
Total number of bits:  8000019627

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:45.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           6.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51249164.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:41.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9988

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7231.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.69
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.66
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:57.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908548
  j =  2                              :            45717
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45861
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869861
  j =  1                              :        399908284
  j =  2                              :            45849
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.96
p-value of test                       :  6.2e-3

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.44
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.41
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.99
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.77
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.98
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.36
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.35
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.23
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.54
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.04
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.03
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.71
p-value of test                       :  1.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.12
p-value of test                       :    0.9991    *****

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.29e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.33
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.85
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10239.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.07
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999936995

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.53
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000126040

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:14.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 82  LempelZiv, r = 0                0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52264972.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9900

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.06
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6946.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.51
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.91
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908059
  j =  2                              :            45966
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907871
  j =  2                              :            46060
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.026
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 5.24e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.52
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.03
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.17
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.85
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.20
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.23
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.73
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.43
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.03
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.31
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.84
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    2.49
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.97
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.93
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.69
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000143671

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.19
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000051346

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.98

 All tests were passed




Server wird beendet - Lösche Semaphor 53280780.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5281
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.66
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.75
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.64
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45578
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869578
  j =  1                              :        399908847
  j =  2                              :            45572
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45599
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869599
  j =  1                              :        399908804
  j =  2                              :            45595
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.38
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.49
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.94
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.43
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.06
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.92
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.34
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.96
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.92
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.46
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.82
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.42
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.96
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.50
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9756.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.30
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999920861

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.63
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999965615

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.12

 All tests were passed




Server wird beendet - Lösche Semaphor 54198284.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7135
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:41.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9937


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.37
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.10
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.36
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.85
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.56
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907687
  j =  2                              :            46152
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908590
  j =  2                              :            45702
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.87e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.38
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.77
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.54
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.87
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.96
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.30
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.49
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.82
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.15
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.21
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.88
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.42
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.12
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.40e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:18.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.63
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12172.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12085.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.57
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000088486

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000008374

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:41.26

 All tests were passed




Server wird beendet - Lösche Semaphor 55246860.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:41.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  303.92
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.13
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5254.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:00.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46199
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870199
  j =  1                              :        399907604
  j =  2                              :            46195
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907887
  j =  2                              :            46052
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.85
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17736.26
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.94
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.27
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.04
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.77
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  304.90
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.39
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.55
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.38
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.27
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11776.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.03
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000157237

Normal statistic for number of bits   :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.61
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999982772

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   0.075
p-value of test                       :    0.47

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.11

 All tests were passed




Server wird beendet - Lösche Semaphor 56295436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7106
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7506
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.94
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9901

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.46
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6896.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.41
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45537
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869537
  j =  1                              :        399908931
  j =  2                              :            45527
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907938
  j =  2                              :            46019
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.09e-3
p-value of test                       :    0.9989

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.89e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  100.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.62
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.11
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.51
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.22
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.12
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.37
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.000
p-value of test                       :    0.50

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.68e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.85
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.12
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.49
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10279.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.33
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.26
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000046360

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.62
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999975998

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.80
p-value of test                       :    0.9974

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.075
p-value of test                       :    0.53

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:05.36

 All tests were passed




Server wird beendet - Lösche Semaphor 57311244.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.75
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.08
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.00
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908013
  j =  2                              :            45989
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908454
  j =  2                              :            45764
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  5.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.51
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.92
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17701.65
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.19
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.90
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.82
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.01
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.37
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.23
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.35
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.06
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.60
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.45
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.35
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.99
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.14
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.09
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.05
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.10
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.80
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.94
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3913.94
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.10
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000027079

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.12
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000078283

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:59.29

 All tests were passed




Server wird beendet - Lösche Semaphor 58294284.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1479
p-value of test                       :  1.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334599
  j =  1                              :        599997042
  j =  2                              :             1479
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.53
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    4.58
p-value of test                       :  4.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.24
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.14
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.89
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.26
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908622
  j =  2                              :            45674
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908256
  j =  2                              :            45869
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.49
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.37
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.78
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.25
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.87
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.21
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.37
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.11
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.50
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.42
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   0.076
p-value of test                       :    0.47

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.00
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:15.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11592.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.92
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000073438

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.95
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999798716

Normal statistic for number of bits   :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.46
p-value of test                       :  5.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.35
p-value of test                       :  9.3e-3

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:55.45

 All tests were passed




Server wird beendet - Lösche Semaphor 59277324.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5543
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:18.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.55
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5152.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:54.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908301
  j =  2                              :            45842
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45624
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869624
  j =  1                              :        399908755
  j =  2                              :            45618
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9926


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:32.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.49e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.26e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.83
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.04
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.21
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.57
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.19
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.42
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.95
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.23
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.07
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  144.92
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.71
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.81
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.68
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.06e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.74
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.80
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.13
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.58
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000040789

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.07
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000048976

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:55.56

 All tests were passed




Server wird beendet - Lösche Semaphor 60260364.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.77
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.66
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:11.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  476.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.41
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908125
  j =  2                              :            45930
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908663
  j =  2                              :            45658
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.40
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.36
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.60
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.15
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.70
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.25
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.43
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.97
p-value of test                       :    0.02

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.80
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999944717

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.50
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000035494

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.03

 All tests were passed




Server wird beendet - Lösche Semaphor 61308940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4181
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.99
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6928.69
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.46
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:22.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:47.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4873.61
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908547
  j =  2                              :            45725
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.31e-6
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.38
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.28
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.65
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :   98.15
p-value of test                       :    0.9992    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.76
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.46
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.16
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.11
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.12
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.56
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.57
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.79
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.77
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9731.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5093.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.67
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.12
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.92
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999788636

Normal statistic for number of bits   :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.28
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000164995

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.080
p-value of test                       :    0.53

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:57.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 H (L=1000, r=0)     0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62324748.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:37.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.58
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7082.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.47
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908075
  j =  2                              :            45955
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908493
  j =  2                              :            45749
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.09
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.12
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.90
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.78
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.76
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.46
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.50
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.76
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.93
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.57
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.71
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.78
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.84
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999864203

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.69
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999789725

Normal statistic for number of bits   :   -1.66
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:22.12

 All tests were passed




Server wird beendet - Lösche Semaphor 42369037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.49
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5200.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908293
  j =  2                              :            45852
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46220
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870220
  j =  1                              :        399907566
  j =  2                              :            46208
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:34.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.29e-6
p-value of test                       :    0.9979

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.79e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.085
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.60
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.12
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.09
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.67
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.76
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  571.11
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.01
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.81
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.22
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.19
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.86
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.51
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.62
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.38
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.57
p-value of test                       :    0.9979


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:19.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.03e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.73
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.86
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.24
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12001.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.26
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999830117

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.72
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000028867

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:48.68

 All tests were passed




Server wird beendet - Lösche Semaphor 43188237.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    3.30
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.96
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1520.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.13
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4857.16
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908793
  j =  2                              :            45593
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908078
  j =  2                              :            45955
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.14e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.74
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.41
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.81
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   79.15
p-value of test                       :  4.5e-5    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.03
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.00
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.36
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.98
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.48
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.24
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4789.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.45
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.90
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.30
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.17
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.63
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.43
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999983363

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.21
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000225079

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.086
p-value of test                       :    0.47

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:37.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 H (L=50, r=0)       4.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44335117.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.34
p-value of test                       :  2.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.29
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.33
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.50
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.42
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5187.53
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908653
  j =  2                              :            45666
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908707
  j =  2                              :            45642
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:33.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :  5.8e-4    *****

Anderson-Darling statistic = A2       :    7.55
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.49e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.33e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17841.85
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.42
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.54
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.64
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.04
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.35
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.37
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.17
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.78
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.81
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.48
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.45
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.95
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.87
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.74e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   24.29
p-value of test                       :  2.0e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.05
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:20.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.86
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.09
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.47
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999906323

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.34
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999881807

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:54.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45219853.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4510
p-value of test                       :  4.6e-3


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.00
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.80
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.37
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:55.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907784
  j =  2                              :            46105
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908196
  j =  2                              :            45896
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.7e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.92
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17120.48
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.11
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.59
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.38
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.03
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.68
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.91
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.12
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.69
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.44
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    3.03
p-value of test                       :  1.2e-3



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.81
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.26
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.52
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.94
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999986126

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.45
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999886862

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:21.70

 All tests were passed




Server wird beendet - Lösche Semaphor 46202893.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997305
  j =  2                              :             1346
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7022
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.73
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907729
  j =  2                              :            46134
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.39
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.25
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  4.7e-4    *****

Anderson-Darling statistic = A2       :    8.34
p-value of test                       :  8.8e-5    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :18179.11
p-value of test                       :  3.8e-5    *****



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.70
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.82
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.87
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.82
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.59
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5151.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.41
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.09
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.52
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10180.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.30
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.72
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000009616

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.47
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000070375

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.026
p-value of test                       :    0.51

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        0.9997 
 73  GCD                             3.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47218701.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.10
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  493.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6959.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:07.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.45
p-value of test                       :    0.9938


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.23
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908313
  j =  2                              :            45842
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45572
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869572
  j =  1                              :        399908859
  j =  2                              :            45566
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.015
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.88
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.66
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17426.06
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.31
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.24
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.53
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.19
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.98
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.95
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.62
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.96
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.06
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.68
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.44e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9760.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10308.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:18.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.2e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3934.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000053908

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.38
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000090844

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:38.63

 All tests were passed




Server wird beendet - Lösche Semaphor 48267277.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:47.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.45
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.20
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46257
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870257
  j =  1                              :        399907488
  j =  2                              :            46253
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907988
  j =  2                              :            46003
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.67e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.62
p-value of test                       :  1.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.11
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17526.82
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.33
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.74
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.06
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.61
p-value of test                       :  3.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.51
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.51
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.47
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.56
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.54
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -2.31
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.76
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 3.30e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.26
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.82
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.46
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000078988

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.18
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999901940

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         : -7.40e-4
p-value of test                       :    0.50

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:07.98
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 57  AppearanceSpacings, r = 0       1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49315853.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    4.10
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:02:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.91
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.27
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.20
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7249.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.59
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.06
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.44
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45609
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869609
  j =  1                              :        399908785
  j =  2                              :            45603
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908905
  j =  2                              :            45543
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.12e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 3.50e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.79
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:51.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.92
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   37.35
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.23
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.59
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.45
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.09
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.79
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.69
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.81
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.60
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.75
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.47
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.33
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.35
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9729.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4680.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.16
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.21
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999933722

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999934436

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:37.47

 All tests were passed




Server wird beendet - Lösche Semaphor 50397197.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     639
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.86
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.53
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907718
  j =  2                              :            46138
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45714
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869714
  j =  1                              :        399908575
  j =  2                              :            45708
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.75e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.41
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.06
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17062.75
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.33
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.73
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.95
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.80
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.67
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.51
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.56
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.98e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.33
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   24.20
p-value of test                       :  2.1e-3

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10167.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:14.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.47
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999966449

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.00
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000129379

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:40.62

 All tests were passed




Server wird beendet - Lösche Semaphor 51445773.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.09
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.59
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.15
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45750
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869750
  j =  1                              :        399908504
  j =  2                              :            45742
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908335
  j =  2                              :            45825
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.50e-4
p-value of test                       :  3.0e-4    *****

Anderson-Darling statistic = A2       :    5.34
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.93
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.21
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17391.86
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.58
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.89
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.69
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  426.12
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.87
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.92
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4770.28
p-value of test                       :    0.9900


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.42
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.71
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.03
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  265.46
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.83
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5162.08
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.82
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.70
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999858584

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.72
p-value of test                       :  8.8e-3


-----------------------------------------------
Total number of bits:  8000114826

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:34.15

 All tests were passed




Server wird beendet - Lösche Semaphor 52494349.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.66
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7181.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.27
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.52
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908848
  j =  2                              :            45567
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907971
  j =  2                              :            46010
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    5.02
p-value of test                       :  2.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9976


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.17e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.64
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.72
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17381.95
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.32
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.12
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.47
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5245.64
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.79
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.91
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.14e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 9.34e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 3.11e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:15.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4744.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.27
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999979679

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.90
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000023287

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:27.01

 All tests were passed




Server wird beendet - Lösche Semaphor 53542925.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.09
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5202.70
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908252
  j =  2                              :            45865
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45385
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869385
  j =  1                              :        399909234
  j =  2                              :            45377
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.91
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17376.59
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.09
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.95
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.76
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.00
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.86
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.36
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.95
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.56
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.02
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.69
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.38
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.03
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.53
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.04
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.80
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    2.53
p-value of test                       :  5.8e-3



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.13e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.42
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.89
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5139.43
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.86
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12158.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999957920

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.59
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999953777

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:25.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54591501.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7074.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.75
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907799
  j =  2                              :            46096
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908817
  j =  2                              :            45587
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.38
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.60
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    8.85
p-value of test                       :    0.9979


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.79
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.24
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.52
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.89
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.51
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.46
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.89
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.27
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.19
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.11
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.34
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.14
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.24
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999893387

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.51
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000115279

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:24.22

 All tests were passed




Server wird beendet - Lösche Semaphor 55771149.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.71
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:20.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:47.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.79
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:20.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.25
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.85
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907834
  j =  2                              :            46077
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:33.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.9901

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.03
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.55
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.22
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.75
p-value of test                       :  9.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.09
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.85
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.34
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.41
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.92
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.51
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.29
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.04e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:29.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11997.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.64
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999956942

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.37
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000162604

Normal statistic for number of bits   :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.80
p-value of test                       :    0.04

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:13.15

 All tests were passed




Server wird beendet - Lösche Semaphor 56819725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.97
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.17
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7152.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.36
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.03
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399909004
  j =  2                              :            45486
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45468
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869468
  j =  1                              :        399909066
  j =  2                              :            45464
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.26e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.89e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.91
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.48
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17721.25
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.38
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.27
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.20
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.15
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.47
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.74
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.64
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.71
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:16.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.09
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.26
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000005941

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.07
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999885275

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:57.60

 All tests were passed




Server wird beendet - Lösche Semaphor 57868301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7131
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9910

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.26
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.04
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.24
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.34
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.83
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:54.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908687
  j =  2                              :            45649
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.6e-3

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.61e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.85
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.87
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.99
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17719.21
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.70
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.91
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.37
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.37
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.13
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.53
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.25
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.88
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.31
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11973.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.77
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999997040

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.01
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000003238

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:27.98

 All tests were passed




Server wird beendet - Lösche Semaphor 58916877.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.89
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.22
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:54.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45549
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869549
  j =  1                              :        399908903
  j =  2                              :            45547
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908152
  j =  2                              :            45915
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.26e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.46e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.82
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.60
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.17
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17347.26
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.83
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.09
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.87
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.22
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.74
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.02
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.02
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.09
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.29
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.97
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.85
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.87
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.27
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.16
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12124.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.58
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000000280

Normal statistic for number of bits   : 2.21e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.08
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999978962

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 47  MaxOft AD, t = 16               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59965453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4197
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7617
p-value of test                       :  2.7e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:02:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.13
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6828.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.04
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:35.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.38
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:00.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908451
  j =  2                              :            45767
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908053
  j =  2                              :            45966
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.98
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.14
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.89
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.94
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.69
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.85
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.60
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.74
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.09
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.56
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.28
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  452.00
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.40
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.59e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.26
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.68
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.58
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9761.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 8.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3925.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.46
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999940151

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.33
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999953972

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :   0.035
p-value of test                       : 1 -  3.9e-6    *****

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:46.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 21  BirthdaySpacings, t = 16        2.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61014029.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.35
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     664
p-value of test                       :  5.3e-3

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.24
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5160.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908797
  j =  2                              :            45600
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45870
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869870
  j =  1                              :        399908264
  j =  2                              :            45862
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.65e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17174.42
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.57
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.80
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.83
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.57
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.15
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.94
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.55
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.14
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.61
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.77
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.98
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.65
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.58
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.95
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.95
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.79
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.19
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999916433

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.88
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000099544

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:51.57

 All tests were passed




Server wird beendet - Lösche Semaphor 62029837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:47.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    3.00
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.40
p-value of test                       :  1.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.97
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.40
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.06
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908640
  j =  2                              :            45674
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:32.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.66
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.84
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.61
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.17
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.33
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.27
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.68
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.08
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.92
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.61
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.71e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.49
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9777.23
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.39
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4281.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.32
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000029092

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.28
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000103483

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         : 8.84e-3
p-value of test                       :    0.50

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:24.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42401806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5292
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.13
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.20e-3
p-value of test                       :    0.9957

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.72
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.00
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:24.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908480
  j =  2                              :            45757
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908457
  j =  2                              :            45764
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:33.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.05
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.76
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.96
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.61
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.18
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.52
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.04
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.51
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.56
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.90
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.087
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4315.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.53
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999946070

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.67
p-value of test                       :    0.9904


-----------------------------------------------
Total number of bits:  8000012382

Normal statistic for number of bits   :   0.098
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:00.79

 All tests were passed




Server wird beendet - Lösche Semaphor 43057166.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5520
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4505
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.80
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5133.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45747
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869747
  j =  1                              :        399908510
  j =  2                              :            45739
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908077
  j =  2                              :            45954
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17309.37
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.56
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.03
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.54
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.42
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.93
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.19
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.11
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.15
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10297.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4747.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3928.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000084184

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.73
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000000505

Normal statistic for number of bits   : 3.99e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:28.48

 All tests were passed




Server wird beendet - Lösche Semaphor 44597262.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:51.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.40
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    3.37
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     118
p-value of test                       :    0.9961

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7261.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:07.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.13
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46044
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870044
  j =  1                              :        399907916
  j =  2                              :            46036
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908413
  j =  2                              :            45786
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.74e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.40e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.88
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17352.83
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.67
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.24
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.17
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.65
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.13
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.85
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.60
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5259.24
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.68
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.30
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.26
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.77e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.65e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.60
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4209.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.49
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999940397

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000015199

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.051
p-value of test                       :    0.52

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:47.04

 All tests were passed




Server wird beendet - Lösche Semaphor 45514766.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.11
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.03
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.26
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.33
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45522
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869522
  j =  1                              :        399908960
  j =  2                              :            45514
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908175
  j =  2                              :            45908
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :  3.8e-4    *****

Anderson-Darling statistic = A2       :    9.16
p-value of test                       :  3.6e-5    *****


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.78
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.30
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.94
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.40
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.45
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.52
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.68
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.29
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.10
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.90
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.19
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.57
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.07
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.50
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.10
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.98
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.36
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.19
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.46
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.71
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.40
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.03
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.58
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3969.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.77
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11976.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999972485

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.68
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999998474

Normal statistic for number of bits   :  -0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:01.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               3.6e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46465038.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.30
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.48
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5000.23
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45653
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869653
  j =  1                              :        399908700
  j =  2                              :            45641
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****


-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.18e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.45
p-value of test                       :  5.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16930.00
p-value of test                       :    0.9965



-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.77
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  557.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.82
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.21
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.16
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.30
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.08
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.89
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.84
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.03
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.21e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.01
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.96
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.22
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.13
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000026596

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.66
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999946124

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:44.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 48  MaxOft AD, t = 24               0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47448078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:42.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:40.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1470.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:28.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.73
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4902.14
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908305
  j =  2                              :            45840
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.97e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.65
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.92
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.89
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.61
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.20
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.44
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.91
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.51
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.81
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.08
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.89
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.49
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4701.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11711.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.62
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.01
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999967928

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.65
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999993644

Normal statistic for number of bits   :  -0.050
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    2.91
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:15.78

 All tests were passed




Server wird beendet - Lösche Semaphor 48496654.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5550
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    2.34
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:32.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.89
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.84
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5173.92
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907941
  j =  2                              :            46025
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908398
  j =  2                              :            45795
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.100
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.39
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.31
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.75
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17294.30
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.23
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.84
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.10
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.45
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.06
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.05
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.94
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.53
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.25
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.97
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.22
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.30
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.78e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.90
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4317.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.05
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000075859

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.89
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000041587

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.21
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:25.15

 All tests were passed




Server wird beendet - Lösche Semaphor 49446926.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5397
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:15.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.06
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:16.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.19
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5168.28
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907838
  j =  2                              :            46078
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46290
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870290
  j =  1                              :        399907422
  j =  2                              :            46286
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.56e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -1.41e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.95
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.75
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.29
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.53
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.27
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.56
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.04
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.41
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.90
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.70
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.01
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.71
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.49
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.73
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.68e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.10
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12104.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000046741

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.75
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999863714

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:39.78

 All tests were passed




Server wird beendet - Lösche Semaphor 50757646.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:40.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1506
p-value of test                       :  8.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334626
  j =  1                              :        599996988
  j =  2                              :             1506
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6792.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.30
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.75
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908407
  j =  2                              :            45795
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908211
  j =  2                              :            45890
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  4.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.46e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.76
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17541.27
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.04
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.93
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.45
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.66
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.41
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.82
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.24
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.57
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.76
p-value of test                       :    0.9970


-----------------------------------------------
Normal statistic for number of jumps  :   0.088
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.74
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.65e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -9.75e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.44
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3941.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.37
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12073.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.45
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000006940

Normal statistic for number of bits   :   0.055
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999970454

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.044
p-value of test                       :    0.48

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           8.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52199438.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.39
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.94
p-value of test                       :  9.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.13
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.75
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  180.57
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.52
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4899.87
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908038
  j =  2                              :            45978
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908155
  j =  2                              :            45915
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.43
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.97
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.88
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.83
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.94
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.09
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.67
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.19
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.59e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.36e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.87
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.79
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10249.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4770.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.15
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.11
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.46
p-value of test                       :    0.9939


-----------------------------------------------
Total number of bits:  7999930848

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.12
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999999566

Normal statistic for number of bits   : -3.43e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    2.62
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:54.90

 All tests were passed




Server wird beendet - Lösche Semaphor 53116942.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.07
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.14
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.17
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.57
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.65
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5220.25
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907850
  j =  2                              :            46072
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46220
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870220
  j =  1                              :        399907565
  j =  2                              :            46210
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    6.46
p-value of test                       :  6.4e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   17.64
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.23
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.22
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.02
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.42
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.44
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.32
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.96
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.71
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.72
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.85
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.44
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.61
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.22
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.52
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.14
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.12
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  247.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.57
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.71
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11737.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.99
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999967439

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.13
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999973751

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54263822.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5317
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.99
p-value of test                       :  8.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.01
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.13
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.04
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   86.74
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4897.73
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45360
p-value of test                       :    0.9924


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869360
  j =  1                              :        399909282
  j =  2                              :            45356
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46231
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870231
  j =  1                              :        399907538
  j =  2                              :            46231
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.39e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 7.80e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.09
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.79
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.87
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.56
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.97
p-value of test                       :    0.9928


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.56
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4796.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.03
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.62
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.67
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.83
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.99
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10271.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.38
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:04:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11527.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.63
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999954443

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.64
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000118780

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.04

 All tests were passed




Server wird beendet - Lösche Semaphor 55312398.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9910


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.12
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6777.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.02
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.94
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.47
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908374
  j =  2                              :            45810
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908085
  j =  2                              :            45953
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.85e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.14e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.84e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.43
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17184.11
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.15
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.63
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.08
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.26
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.82
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.57
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.11
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.39
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.56
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  458.15
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.91
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.20
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.35
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12104.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.77
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000044755

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.86
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000036154

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.14

 All tests were passed




Server wird beendet - Lösche Semaphor 56229902.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997353
  j =  2                              :             1322
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4214
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     834
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.32
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.53
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908224
  j =  2                              :            45879
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908871
  j =  2                              :            45563
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.10e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.85
p-value of test                       :  1.0e-2

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.51e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17079.62
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.57
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.02
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.26
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.02
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.82
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.37
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.91
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.49
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.45
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.80
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.57
p-value of test                       :    0.9979


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.78
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.80
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.12
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999919391

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.24
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999946502

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.54
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.064
p-value of test                       :    0.47

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:20.39

 All tests were passed




Server wird beendet - Lösche Semaphor 57245710.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.94
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.61
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.19
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:57.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908528
  j =  2                              :            45733
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908112
  j =  2                              :            45938
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:29.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17530.76
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.26
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.51
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.60
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.51
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.58
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.82
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.59
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.51
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  143.08
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.86
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.25
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.39
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :3.51e-17
p-value of test                       :    0.50

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   32.65
p-value of test                       :  7.1e-5    *****

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.26
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9708.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.57
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.13
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.83
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000055735

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.21
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999995588

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.61
p-value of test                       :  4.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.70
p-value of test                       :    0.9965

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:15.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    0.9991 
 86  LongestHeadRun, r = 0           7.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58392590.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.81
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  498.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6852.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.68
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.22
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907733
  j =  2                              :            46132
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45334
p-value of test                       :    0.9946


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869334
  j =  1                              :        399909336
  j =  2                              :            45326
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 6.55e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.42
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.23
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.22
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17770.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.43
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.37
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.58
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.00
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.18
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.08
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.21
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.30
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.91e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.72e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.59
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.40
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9864.71
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9984.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:33.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.98
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.91
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11947.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.53
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000048493

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.77
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999978041

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:39.79

 All tests were passed




Server wird beendet - Lösche Semaphor 59408398.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.33

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5333
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.99
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.93
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7034.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.55
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.00
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908772
  j =  2                              :            45611
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907919
  j =  2                              :            46039
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.76
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.98
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.44
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.03
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.57
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5187.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.76
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.05
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.71
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.22
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.13
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.06
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10102.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4014.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11487.63
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.16
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000130450

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.54
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000047089

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:13.36

 All tests were passed




Server wird beendet - Lösche Semaphor 60555278.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.17
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.61
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.28
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908121
  j =  2                              :            45938
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17057.87
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.06
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.19
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.74
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.46
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.71
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.04
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.94
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.26
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.86
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.24
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.11
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9661.69
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.70
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999864854

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.42
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000091288

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.21
p-value of test                       :    0.9925

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:20.94

 All tests were passed




Server wird beendet - Lösche Semaphor 61505550.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.08
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.96
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.88
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.72
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.79
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5138.16
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:01.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908190
  j =  2                              :            45902
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907883
  j =  2                              :            46054
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.93e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.06
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.06
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.47
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.90
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.30
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.26
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.41
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.07
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.00
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.41
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:17.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.41
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.92e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.80
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.59
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.16
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5192.40
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4357.53
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.55
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.95
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000047182

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.91
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000128662

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:03:09.52
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62652430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:33.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.04
p-value of test                       :  3.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.74
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.44
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.78
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.83
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4815.87
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908757
  j =  2                              :            45620
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46133
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870133
  j =  1                              :        399907738
  j =  2                              :            46125
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.80e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:42.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.53
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.92
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.84
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.19
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.14
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.02
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.37
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.12
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.30
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.20
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.59
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.62
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:33.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:33.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.10
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9736.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:20.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.90
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999891806

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.15
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000061375

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:00.87

 All tests were passed




Server wird beendet - Lösche Semaphor 42434575.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7096
p-value of test                       :    0.9954


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9969

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    3.24
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.52
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907602
  j =  2                              :            46196
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908362
  j =  2                              :            45813
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.78
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17591.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.91
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.14
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.85
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  186.29
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.61
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.85
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.45
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.20
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.82
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.79
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.05
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.98
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.40e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.41
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.59
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:11.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.43
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.79
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.66
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000046273

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.28
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999881828

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:01.32

 All tests were passed




Server wird beendet - Lösche Semaphor 43646991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5322
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.26
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  337.38
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.63
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.82
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46096
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870096
  j =  1                              :        399907810
  j =  2                              :            46092
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46065
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870065
  j =  1                              :        399907875
  j =  2                              :            46055
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.96e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.96
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.56
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.92
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.96
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.06
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.21
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.27
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.41
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.94
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.96
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.17
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.97
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.26
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4614.81
p-value of test                       : 1 -  3.9e-5    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.85
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.44
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9906

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.57
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.45
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.54
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000110779

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.16
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999923534

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:11.53
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     0.9998 
 79  RandomWalk1 J (L=10000, r=15)  1 -  3.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44433423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    6.19
p-value of test                       :  8.1e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     268
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.44
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.87
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.89
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.05
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:01.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907877
  j =  2                              :            46060
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908549
  j =  2                              :            45721
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.36e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.62
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.38
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.56
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.53
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.36
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.12
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.98
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.76
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.37
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.93
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.17
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.63
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.45
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.60
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.94
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4602.30
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11668.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.61
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000048997

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.42
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999843512

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.20

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          8.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45252623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9980


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1322.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.42
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.36
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:55.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908381
  j =  2                              :            45805
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 3.39e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.37
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17505.00
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:52.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.28
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.31
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.64
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.46
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.70
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.39
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.85
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.77
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.47
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.43
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    3.92
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.89
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.30
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.96
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12302.82
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.22
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999805052

Normal statistic for number of bits   :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999891335

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.019
p-value of test                       :    0.49

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.62

 All tests were passed




Server wird beendet - Lösche Semaphor 46268431.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    3.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.43
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5217.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907980
  j =  2                              :            46007
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46390
p-value of test                       :  8.7e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870390
  j =  1                              :        399907223
  j =  2                              :            46384
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:20.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.01
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.86
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.33
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.48
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.42
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.90
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.82
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.05
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.64
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.22
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.00
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.12
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.08
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.01
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.019
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5089.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.00
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.90
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000109492

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.60
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000008611

Normal statistic for number of bits   :   0.068
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.80

 All tests were passed




Server wird beendet - Lösche Semaphor 47251471.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5584
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.00
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.23
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.03
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.64
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.02
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.56
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:54.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908284
  j =  2                              :            45852
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908776
  j =  2                              :            45606
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.04
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.37
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.50
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.33
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.22
p-value of test                       :  9.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.75
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.96
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.17
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.42
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.85
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.20
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.06
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.15
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.71
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.17
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999831245

Normal statistic for number of bits   :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.80
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000056962

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:11.86

 All tests were passed




Server wird beendet - Lösche Semaphor 48300047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9929

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9952

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:07.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.69
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4837.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:54.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908971
  j =  2                              :            45513
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908318
  j =  2                              :            45841
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.02
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.81
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.89
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.32
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.56
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.02
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.21
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.10
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.51
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.31
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.62
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.15
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.29
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.00
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    2.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.74
p-value of test                       :  7.9e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.84
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12521.79
p-value of test                       :  4.3e-6    *****

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.57
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999990653

Normal statistic for number of bits   :  -0.074
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.62
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000055615

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.24
p-value of test                       :    0.01

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      4.3e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49348623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5415
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.53
p-value of test                       :  5.0e-3

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9931

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:17.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  485.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46074
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870074
  j =  1                              :        399907859
  j =  2                              :            46060
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907829
  j =  2                              :            46078
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.44
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17739.43
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.24
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.68
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.53
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.63
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.69
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.14
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.58
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.21
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.91
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.36
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:34.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.99
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:21.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.44
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.21
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  146.39
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9742.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.81
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.68
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11621.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.75
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000080137

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.17
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000070015

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.31

 All tests were passed




Server wird beendet - Lösche Semaphor 50364431.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.18
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.42
p-value of test                       :  5.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.64
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.00
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.12
p-value of test                       :  9.8e-3


-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.97
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908704
  j =  2                              :            45642
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46142
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870142
  j =  1                              :        399907716
  j =  2                              :            46142
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.41e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.68
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.43
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.11
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.00
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.96
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.33
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.67
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.66
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.65
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.94
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.64
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.98
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  464.00
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.43
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.14
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.01
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.73
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000028435

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.90
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000108358

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    2.49
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.27

 All tests were passed




Server wird beendet - Lösche Semaphor 51413007.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5561
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   54.40
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.76
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.55
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45695
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869695
  j =  1                              :        399908612
  j =  2                              :            45691
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908244
  j =  2                              :            45878
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  3.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.76
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.69
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.09
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.20
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.33
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.28
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.64
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.80
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.51
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -2.56
p-value of test                       :    0.9947



-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.37
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.12e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.32e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.57
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10213.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10191.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:16.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.62
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000002293

Normal statistic for number of bits   :   0.018
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.11
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999874880

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:48.15

 All tests were passed




Server wird beendet - Lösche Semaphor 52461583.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.29
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.49
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1516.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:19.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.76
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5073.11
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908880
  j =  2                              :            45548
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908438
  j =  2                              :            45778
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.88
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.02
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:42.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17656.76
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.56
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.86
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.76
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.60
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.80
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.18
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.73
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.68
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.17
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.45
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.70
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.43
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.85
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.73
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9982

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.63
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000024505

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.29
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000109393

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:50.28

 All tests were passed




Server wird beendet - Lösche Semaphor 53510159.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5646
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7581
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    6.47
p-value of test                       :  6.2e-4    *****

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    4.03
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.38
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   86.65
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.08
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.33
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5273.55
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908204
  j =  2                              :            45889
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 4.88e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   95.45
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.32
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.66
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.34
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.64
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.79
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   89.32
p-value of test                       :    0.9993    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.77
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.46
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.16
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.19
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.92
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.18
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.59
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.72e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.99
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.91
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.29
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:16.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4949.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12130.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.07
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999959009

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.30
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000059575

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           6.2e-4
 77  RandomWalk1 R (L=1000, r=20)    0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54558735.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.92
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.29
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908474
  j =  2                              :            45760
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908207
  j =  2                              :            45892
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.73e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   16.42
p-value of test                       :  2.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17202.14
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.54
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.77
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.01
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.58
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.96
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.81
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.32
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.53
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.98e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.85e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.47
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.91
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.09
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11513.62
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.92
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000037522

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.64
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000048541

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.41

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 71  MatrixRank, L=5000              2.7e-4
 93  HammingCorr, L = 300            0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55607311.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    4.95
p-value of test                       :  3.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7106.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.90
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.03
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.95
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908017
  j =  2                              :            45990
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908540
  j =  2                              :            45727
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   32.65
p-value of test                       :    0.9999    *****

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.57
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.59
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17422.19
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.01
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.53
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.66
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.13
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.85
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.74
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.20
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.73
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.57
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.86
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.98
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.45
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.10e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.59
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9791.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.55
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999956273

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.39
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000119281

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.10
p-value of test                       :    0.02

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.59
p-value of test                       :  4.8e-3

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:11.11
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56655887.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.65
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.72
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.96
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7223.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.10
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.00
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.95
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908874
  j =  2                              :            45560
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45580
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869580
  j =  1                              :        399908840
  j =  2                              :            45580
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-4
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.86
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.34
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.13
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.16
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.14
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.54
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.03
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.31
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.44
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4778.45
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.10
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.59
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.11
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.05e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  259.93
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.79
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.74
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4282.09
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:33.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.38
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000054916

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.39
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999874928

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:41.30

 All tests were passed




Server wird beendet - Lösche Semaphor 57704463.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.64
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     969
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.83
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.00
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.99
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:53.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908352
  j =  2                              :            45818
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45700
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869700
  j =  1                              :        399908600
  j =  2                              :            45700
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.60e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17216.56
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.67
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.17
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.25
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.50
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.44
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.19
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.92
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.51
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.42
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.54
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.28
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.19
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.88
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.93
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999934622

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.20
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999999641

Normal statistic for number of bits   : -2.84e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.00
p-value of test                       :    0.02

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.97

 All tests were passed




Server wird beendet - Lösche Semaphor 58753039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5290
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9947

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.55
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6782.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.04
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.56
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908706
  j =  2                              :            45638
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908841
  j =  2                              :            45575
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.74e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.61e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.42
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.20
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17083.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.57
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.90
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.12
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.57
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.44
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.04
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.20
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.08
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.89
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.59
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.11
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.04
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.83
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.86
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.81
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.17
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4834.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.90
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.48
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.84e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.11
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    3.51
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:11.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.35
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000055462

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.03
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000121639

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:48.86

 All tests were passed




Server wird beendet - Lösche Semaphor 59801615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:15.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6804.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.14
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.74
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.45
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46197
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870197
  j =  1                              :        399907608
  j =  2                              :            46193
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908163
  j =  2                              :            45911
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  4.7e-5    *****

Anderson-Darling statistic = A2       :    6.62
p-value of test                       :  5.3e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.53e-4
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.55
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17596.45
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.95
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.94
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.16
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.00
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.08
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.38
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.10e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 7.04e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.73e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.83
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.30
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.46
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.99
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.64
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.12
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999917471

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.27
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000023725

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         : 1.06e-3
p-value of test                       :    0.50

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.06

 All tests were passed




Server wird beendet - Lösche Semaphor 60850191.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:10.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.67
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.28
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.84
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.57
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.88
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.73
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908276
  j =  2                              :            45856
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.38
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.04
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.22
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.77
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.17
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.75
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.17
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  442.05
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.75
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.34
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.57
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.20
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.28e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.28
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  242.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10177.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.73
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.08
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.15
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.30
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999926687

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.71
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000019252

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : -3.14e-3
p-value of test                       :    0.50

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:04.45

 All tests were passed




Server wird beendet - Lösche Semaphor 61898767.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1482
p-value of test                       :  8.6e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334602
  j =  1                              :        599997036
  j =  2                              :             1482
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.23
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    3.08
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.14
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.88
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  514.39
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7130.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.74
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.01
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45754
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869754
  j =  1                              :        399908493
  j =  2                              :            45752
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:32.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.11e-5
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:45.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.13
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17569.05
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.04
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.89
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.76
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.00
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.81
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.69
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.28
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.00
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.75
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.91
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.15
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:14.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.66e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.01
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:04:20.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.64
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.25
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000129256

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.07
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000028018

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:12.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42467344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.25
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.03
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.60
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.64
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.41
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5178.01
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45737
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869737
  j =  1                              :        399908527
  j =  2                              :            45735
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:20.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.45e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.95
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.58
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17304.85
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.72
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.51
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.79
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.88
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.33
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.86
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.19
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.07
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.85
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.75
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.34
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    2.74
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.57e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.02
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    4.65
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  149.30
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:02:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3923.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.00
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999935948

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.73
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000070996

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.16

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:00.65

 All tests were passed




Server wird beendet - Lösche Semaphor 43417616.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    4.56
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.75
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.34
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.05
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45900
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869900
  j =  1                              :        399908206
  j =  2                              :            45888
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46141
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870141
  j =  1                              :        399907722
  j =  2                              :            46133
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.19e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.62
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.16
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.52
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.74
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.78
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  433.01
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.56
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.32
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.59
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.67
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.59
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.58
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.66
p-value of test                       :    0.9961

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.22
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4622.99
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11436.14
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.24
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000225400

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.83
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000086788

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:39.44

 All tests were passed




Server wird beendet - Lösche Semaphor 45023248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5426
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:52.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.59
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.96
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5016.50
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907743
  j =  2                              :            46124
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908162
  j =  2                              :            45913
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.09e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 2.35e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17125.31
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.35
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.06
p-value of test                       :    0.9927


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.25
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.23
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.48
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.76
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.10
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.30
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    2.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.82
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.52
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.16
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999872363

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.85
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999902759

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:21.82

 All tests were passed




Server wird beendet - Lösche Semaphor 46039056.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5388
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.79
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.61
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.69
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.69
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4823.96
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45644
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869644
  j =  1                              :        399908714
  j =  2                              :            45640
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908017
  j =  2                              :            45981
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17637.38
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.52
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.08
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.43
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.91
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.35
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.97
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.11
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.08
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.52
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.52
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.65
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.29
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.09e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.89
p-value of test                       :  5.1e-3

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9873.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.90
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.69
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12121.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.32
p-value of test                       :  3.4e-3


-----------------------------------------------
Total number of bits:  7999874841

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.72
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999919109

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.014
p-value of test                       :    0.49

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:23.01

 All tests were passed




Server wird beendet - Lösche Semaphor 46956560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7486
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    3.51
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  367.41
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7021.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:54.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908249
  j =  2                              :            45868
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -5.09e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.68
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.14
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.42
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.63
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.46
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.82
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.71
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.65
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.78
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.59
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.96
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.61
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.19
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.44
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.64
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.97
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.63
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.55e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.43
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.93
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.55
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:34.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.42
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000137617

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.12
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999865559

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:25.05

 All tests were passed




Server wird beendet - Lösche Semaphor 47939600.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:34.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:34.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    3.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.30
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45815
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869815
  j =  1                              :        399908372
  j =  2                              :            45811
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908086
  j =  2                              :            45945
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.63e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.90
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.62
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.74
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.49
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.22
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.60
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.14
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.30
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.99
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.42
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.98
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.46
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.88
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10203.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.83
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11817.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.01
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999984329

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.83
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999987410

Normal statistic for number of bits   :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:14.78

 All tests were passed




Server wird beendet - Lösche Semaphor 49053712.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.40
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    3.29
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  515.72
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.20
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5043.22
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908159
  j =  2                              :            45919
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908660
  j =  2                              :            45667
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.71e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.90
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   75.75
p-value of test                       :  5.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17275.79
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.04
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.32
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.16
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.07
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.91
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  200.83
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  490.41
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.60
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.73
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.75
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.90e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.31
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9814.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:12.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11606.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.79
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000169312

Normal statistic for number of bits   :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.18
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999992489

Normal statistic for number of bits   :  -0.059
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:29.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          5.5e-4
 77  RandomWalk1 R (L=1000, r=20)    2.5e-4
 78  RandomWalk1 H (L=10000, r=0)    1.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50036752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5365
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    4.05
p-value of test                       :  8.3e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     673
p-value of test                       :  1.8e-3

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.33
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.53
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5171.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908010
  j =  2                              :            45989
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:29.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.14
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.81
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.69
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.31
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.68
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.75
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.42
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.78
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.98
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.46
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.21
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.61
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.31
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    2.02
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.28
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 2.87e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.56
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9805.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10233.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.02
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000024637

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.90
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000033025

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:19.50

 All tests were passed




Server wird beendet - Lösche Semaphor 51052560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7047.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.32
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:57.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907546
  j =  2                              :            46224
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908110
  j =  2                              :            45942
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.91e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.99e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.03
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.89
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.65
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.67
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.50
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.91
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.16
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.07
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.03
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.81
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.79
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.26
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.77
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.40
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.38
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.26
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.93
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.09
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.57
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.60
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.95
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.49
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.08
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999954002

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.20
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000037759

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:26.54

 All tests were passed




Server wird beendet - Lösche Semaphor 51970064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1218
p-value of test                       : 1 -  3.0e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334338
  j =  1                              :        599997564
  j =  2                              :             1218
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5325
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.64
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.67
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.89
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45590
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869590
  j =  1                              :        399908821
  j =  2                              :            45588
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907818
  j =  2                              :            46088
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.04
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17159.28
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.71
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.86
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.76
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.90
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.39
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.97
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.23
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.89
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.05
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.23
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.52
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.50
p-value of test                       :    0.9982


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.44e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.22
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9671.54
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.40
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000012079

Normal statistic for number of bits   :   0.095
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.47
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999965462

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:14.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21          1 -  3.0e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52887568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1201
p-value of test                       : 1 -  3.5e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334321
  j =  1                              :        599997598
  j =  2                              :             1201
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:16.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.76
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1553.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6863.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:10.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.46
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.98
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45906
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869906
  j =  1                              :        399908189
  j =  2                              :            45904
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46311
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870311
  j =  1                              :        399907385
  j =  2                              :            46297
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.56e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.29e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.16
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.11
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.72
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.27
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.09
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.87
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.84
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.20
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.37
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.96
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.70
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.51
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9745.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11709.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12072.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.80
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000055861

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.91
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000026554

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:31.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3           1 -  3.5e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53903376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7125
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.67
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.87
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  497.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.12
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.86
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907834
  j =  2                              :            46071
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908448
  j =  2                              :            45770
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.71e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.45
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.87
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.38
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.02
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.44
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  119.93
p-value of test                       :  5.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.47
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4900.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.93
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.37
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.84
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.50
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.02
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.63e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.89
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.79
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999841220

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000085396

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.15
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         : 8.42e-3
p-value of test                       :    0.50

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:52.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 C (L=1000, r=20)    5.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54919184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1252
p-value of test                       :    0.9989

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334372
  j =  1                              :        599997496
  j =  2                              :             1252
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:11.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     830
p-value of test                       :    0.9904

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.15
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.50
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.61
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:57.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908288
  j =  2                              :            45847
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908127
  j =  2                              :            45935
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:20.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.63
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:01:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.46
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.77
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.31
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.96
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.92
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.07
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.83
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.01
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  307.31
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.27
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.05
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.68
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.87e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11648.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.38
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999955223

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.46
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000059008

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:51.97

 All tests were passed




Server wird beendet - Lösche Semaphor 55967760.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.84
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908305
  j =  2                              :            45846
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908227
  j =  2                              :            45882
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.54
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.92
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.10
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.95
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.86
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.45
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.53
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.14
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.29
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.17
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.72
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.29
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.28
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.68e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.39
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9932.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.52
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11863.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11801.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.02
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000032230

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.74
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000183982

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:53.11

 All tests were passed




Server wird beendet - Lösche Semaphor 57049104.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.54
p-value of test                       :  5.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.50
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.90
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.92
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.93
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.28
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908497
  j =  2                              :            45741
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907815
  j =  2                              :            46088
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:32.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.47e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.48
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.50
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.44
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.17
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.23
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.28
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.13
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.74
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.50
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.31
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.54
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.18
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.42
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.98
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.76
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.78
p-value of test                       :    0.9972


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.05
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.97
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.1e-3

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.54
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.32
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.98
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.37
p-value of test                       :  5.1e-3


-----------------------------------------------
Total number of bits:  7999851186

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.82
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000093565

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.54
p-value of test                       :  5.5e-3

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:36.86

 All tests were passed




Server wird beendet - Lösche Semaphor 58064912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5423
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.99
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    4.30
p-value of test                       :  6.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     330
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.69
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.42
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7122.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.17
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:54.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45423
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869423
  j =  1                              :        399909160
  j =  2                              :            45411
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45838
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869838
  j =  1                              :        399908327
  j =  2                              :            45832
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.98
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.30
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.75
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.85
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.75
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.84
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17338.84
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.03
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.06
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.09
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.63
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.78
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.93
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5225.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.29
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.68
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.31
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:40.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.97
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    3.05
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:04:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.49
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:33.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.82
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999860162

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000038068

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:15.04

 All tests were passed




Server wird beendet - Lösche Semaphor 59244560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9943

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.05
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.92
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.95
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:20.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:47.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.35
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.06
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:56.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908755
  j =  2                              :            45621
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908224
  j =  2                              :            45885
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.77e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.25
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.88
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.34
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.15
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.66
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.78
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.56
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.31
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.02
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.09
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.62
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.85
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.70
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9945

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.84e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.60
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.56
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:00.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4264.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.09
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000047512

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.37
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999996038

Normal statistic for number of bits   :  -0.031
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:29.29

 All tests were passed




Server wird beendet - Lösche Semaphor 60424208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1480
p-value of test                       :  1.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334600
  j =  1                              :        599997040
  j =  2                              :             1480
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5252
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9969

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   84.98
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.13
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.39
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908689
  j =  2                              :            45648
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908672
  j =  2                              :            45661
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:32.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.11e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17816.53
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.75
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.34
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.69
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.05
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.05
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.77
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.45e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.69
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999923609

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.33
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000006280

Normal statistic for number of bits   :   0.050
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.77e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.89
p-value of test                       :    0.97

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.45

 All tests were passed




Server wird beendet - Lösche Semaphor 61571088.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5537
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    4.57
p-value of test                       :  4.6e-3

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.72
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.64
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.03
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.04
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.15
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:35.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.55
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908497
  j =  2                              :            45747
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908649
  j =  2                              :            45671
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17135.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.29
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.39
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.19
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4717.07
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.01
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.08
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 3.72e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.99
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.71
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11868.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12016.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.99
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000161305

Normal statistic for number of bits   :    1.28
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.66
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000009892

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.25
p-value of test                       :    0.99

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:34.86

 All tests were passed




Server wird beendet - Lösche Semaphor 62586896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7103
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    3.21
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.82
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.94
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.28
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.81
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.11
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.33
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5207.86
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908083
  j =  2                              :            45951
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907791
  j =  2                              :            46100
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.44e-4
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.15
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.87
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.03
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.95
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.91
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.95
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.55
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  100.79
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.52
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.90
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.86
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.32
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.78
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.44
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.98
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.20
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.48
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.42
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.63
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.24
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000092554

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.81
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000116521

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.97

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:13.32

 All tests were passed




Server wird beendet - Lösche Semaphor 42500113.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     339
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.75
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.64
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.99
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45330
p-value of test                       :    0.9949


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869330
  j =  1                              :        399909344
  j =  2                              :            45322
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908340
  j =  2                              :            45821
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:34.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.95
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.69
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.71
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.51
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.78
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.21
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.66
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.42
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.58
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.52
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.94
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.83
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.44
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  145.80
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.49
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.72
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.36
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12041.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.68
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999958346

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.52
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000143041

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:36.09

 All tests were passed




Server wird beendet - Lösche Semaphor 43286545.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9905

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.13
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.68
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.56
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.68
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:01.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45949
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869949
  j =  1                              :        399908105
  j =  2                              :            45943
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907972
  j =  2                              :            46008
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 4.70e-4
p-value of test                       :  1.5e-4    *****

Anderson-Darling statistic = A2       :    7.07
p-value of test                       :  3.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.00
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    5.04
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   64.57
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17408.04
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.52
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.75
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.44
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.10
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.08
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.39
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.01
p-value of test                       :    0.9952


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.65
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.67
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.61
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.26
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:34.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.67
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.33
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999906272

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.47
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000137377

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:31.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               3.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44236817.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    4.12
p-value of test                       :  7.6e-3

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.46
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.25
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  174.59
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6958.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.24e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.41
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:01.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45835
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869835
  j =  1                              :        399908335
  j =  2                              :            45825
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908827
  j =  2                              :            45579
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:40.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.42
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.88
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.36
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.42
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.82
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.88
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.81
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.60
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.74
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.48
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.44
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.09
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.60
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.53
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4843.35
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.40
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.40
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.91
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.42
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.24
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.52
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    2.12
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.81
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.09
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.02
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.95
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.62
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999914225

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.27
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999977288

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:03.87

 All tests were passed




Server wird beendet - Lösche Semaphor 45711377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9948

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.47
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6802.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.20
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.41
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46112
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870112
  j =  1                              :        399907779
  j =  2                              :            46106
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907752
  j =  2                              :            46118
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.28e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.84e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.54
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.83
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17512.81
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.06
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.53
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.44
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.82
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.39
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.81
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.29
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.00
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.38
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.18
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.31
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.53
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.24e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:20.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.43
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.14
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000040555

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.93
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000007750

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:11.45

 All tests were passed




Server wird beendet - Lösche Semaphor 46628881.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    4.26
p-value of test                       :  6.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.06
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.86
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.67
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.88
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.42
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907923
  j =  2                              :            46034
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908642
  j =  2                              :            45670
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:20.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.52e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.72e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.27
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17664.05
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.12
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.95
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.50
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.36
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.18
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.03
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.14
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.87
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.65
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.32
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.05
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.48e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.17
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.15
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11995.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.60
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000052519

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.12
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000096142

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:45.09

 All tests were passed




Server wird beendet - Lösche Semaphor 47644689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   82.26
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908266
  j =  2                              :            45864
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45894
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869894
  j =  1                              :        399908217
  j =  2                              :            45884
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17121.43
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.48
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.71
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.46
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.36
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.91
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.76
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.94
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.84
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.96
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5077.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.27
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9908

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.38
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.48
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11350.72
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.69
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999850604

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.39
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000036511

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    0.13
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:57.22
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48857105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:41.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.15
p-value of test                       :    0.9984

Stat. AD after spacings (mNP2-S)      :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.44
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.37
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.04
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:05.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907703
  j =  2                              :            46141
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908396
  j =  2                              :            45793
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.1e-3


-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.91e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.54e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.051
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.92
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.30
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.91
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.43
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.02
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.39
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.27
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.92
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.88
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.37
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.21
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.86
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.91
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.01
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.04
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    2.11
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.14
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.21e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.05
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.099
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4291.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.01
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000080665

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.11
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000190228

Normal statistic for number of bits   :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Tests on the sum of all N observations
Standardized normal statistic         :  -0.034
p-value of test                       :    0.51

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:05.37

 All tests were passed




Server wird beendet - Lösche Semaphor 49840145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.23
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.21
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.02
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4924.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45384
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869384
  j =  1                              :        399909233
  j =  2                              :            45382
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46081
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870081
  j =  1                              :        399907844
  j =  2                              :            46069
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.09e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9923


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17616.33
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.84
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.02
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.35
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.41
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.41
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.10
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.24
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.67
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.79
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.21
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.69
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.54
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.77
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.64
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.20
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.47
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.27
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.38
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.37
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4664.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.26
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999970145

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.19
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999956222

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.073
p-value of test                       :    0.53

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.59

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:40.03

 All tests were passed




Server wird beendet - Lösche Semaphor 50855953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    4.95
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.78
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.61
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.32
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.05
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.75
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.19
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908152
  j =  2                              :            45915
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908195
  j =  2                              :            45898
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:52.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.90
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.66
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.70
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.48
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.52
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.95
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.48
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.17
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.67
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.92
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.08
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.97
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.76
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.00
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.98
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.14
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.37
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.58
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9715.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:29.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.32
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.48
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000017149

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.93
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000031009

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:41.93

 All tests were passed




Server wird beendet - Lösche Semaphor 51740689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:11.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:30.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:11.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.14
p-value of test                       :  2.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.97
p-value of test                       :  9.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.58
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.14
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:34.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.95
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.46
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908115
  j =  2                              :            45938
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:33.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    4.19
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:13.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.29
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.31
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.99
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.22
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.95
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.02
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.16
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.57
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.58
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.26
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.99
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.82
p-value of test                       :  8.2e-3


-----------------------------------------------
Normal statistic for number of jumps  :    2.23
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.78e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.96
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:13.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3963.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11811.83
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.39
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999971624

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.14
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999972719

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:52.38

 All tests were passed




Server wird beendet - Lösche Semaphor 52953105.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:05:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    4.30
p-value of test                       :  6.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.67
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  495.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6796.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.27
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.97
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.07
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907685
  j =  2                              :            46156
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908268
  j =  2                              :            45860
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  5.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.64e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.23
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.70
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17326.21
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.97
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.38
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.62
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.75
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.83
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.30
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.23
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.15
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.18
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.17
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.76
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.42
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.95
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.52
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.59e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.27
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4721.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4261.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12055.38
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.61
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999903248

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   94.00
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
Total number of bits:  7999955124

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:17:31.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53936145.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.01
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6845.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.54
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.66
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:01.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908572
  j =  2                              :            45708
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907893
  j =  2                              :            46046
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 6.29e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-5
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.21
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.83
p-value of test                       :  2.4e-3

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.12
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.19
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.37
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.71
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.46
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.20
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.85
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.68
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.82
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.26
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.81
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.20
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.44
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.69
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.97
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    1.59
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.85
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.12e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.46
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.57
p-value of test                       :  5.8e-3

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12003.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.23
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999977879

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   83.84
p-value of test                       :  5.7e-3


-----------------------------------------------
Total number of bits:  7999852740

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.067
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:57.12

 All tests were passed




Server wird beendet - Lösche Semaphor 54984721.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7535
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.83
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6869.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   94.21
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.34
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.12
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5150.87
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908235
  j =  2                              :            45875
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908499
  j =  2                              :            45743
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.84e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 3.26e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.94
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17522.15
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.37
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.67
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.17
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.88
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.59
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.54
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.46
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.32
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.62
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.16
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.55
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.91
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.26
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999784064

Normal statistic for number of bits   :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000082795

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.68

 All tests were passed




Server wird beendet - Lösche Semaphor 56000529.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  378.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1521.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7039.03
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.88
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.90
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.31
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45423
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869423
  j =  1                              :        399909159
  j =  2                              :            45413
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907567
  j =  2                              :            46212
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    : 1.58e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    5.15
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:02:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.83e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.010
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.97
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.36
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16958.61
p-value of test                       :    0.9945



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.44
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.41
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.09
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.61
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.36
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.39
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.59
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.61
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.85
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.74
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.50
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -2.77
p-value of test                       :    0.9972



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.64
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.18e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.94e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.03
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.19
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.42e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10229.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:20.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4780.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.65
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.10
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999866135

Normal statistic for number of bits   :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.40
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999873116

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.12

 All tests were passed




Server wird beendet - Lösche Semaphor 56983569.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    4.55
p-value of test                       :  4.7e-3

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    4.47
p-value of test                       :  5.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.95
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.07
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.86
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.79
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.78
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4888.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907993
  j =  2                              :            45993
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908176
  j =  2                              :            45906
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.06e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.16
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.16
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:52.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.71
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.11
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.50
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.17
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.52
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.00
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.33
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.30
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.45
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.88
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.17
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.58
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.02e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.22e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.75
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.3e-4    *****

Anderson-Darling statistic = A2       :    5.95
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  265.52
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.9936

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.43
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000099094

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.81
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000118012

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.62

 All tests were passed




Server wird beendet - Lösche Semaphor 57999377.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.12
p-value of test                       :    0.9997    *****

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7055.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.64
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.10
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.06
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908267
  j =  2                              :            45862
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908197
  j =  2                              :            45894
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.98e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.80
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.40
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.94
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.42
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.85
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.48
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.01
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.36
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.31
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.35
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.80
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.35
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.94
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.74
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.22
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.37
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.02
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.17
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.53
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.92
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999937334

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.23
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000049411

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:08.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59047953.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7115
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.90
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.15
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6781.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.68
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.61
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.87
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.64
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907985
  j =  2                              :            46003
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45919
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869919
  j =  1                              :        399908166
  j =  2                              :            45911
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.17e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.53
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.73
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.30
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.59
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.46
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.85
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.94
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.19
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.13
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.20
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.72
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.93
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.93
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.79
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.60
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.43
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.02
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:04:34.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4681.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.41
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999918938

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.25
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000076219

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    2.83
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:46.67

 All tests were passed




Server wird beendet - Lösche Semaphor 60063761.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:00.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:10.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.98
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4883.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45608
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869608
  j =  1                              :        399908791
  j =  2                              :            45594
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908144
  j =  2                              :            45922
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:32.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.69e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.066
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.89
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.13
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.60
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17718.29
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.30
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.54
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.77
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.99
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.96
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.13
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5204.95
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.64
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.38
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.24
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.29
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.56
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.11
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4762.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.82
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11536.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.95
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999840488

Normal statistic for number of bits   :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999834887

Normal statistic for number of bits   :   -1.31
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:21.37

 All tests were passed




Server wird beendet - Lösche Semaphor 61177873.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    3.92
p-value of test                       :  9.5e-3

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.63
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  191.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.94
p-value of test                       :  7.0e-3


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.32
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4951.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907973
  j =  2                              :            46009
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908401
  j =  2                              :            45789
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.37e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.79
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.60
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.28
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.99
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.15
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.03
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.50
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4796.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.51
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.14
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.31
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.41
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.38
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10225.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4267.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999861512

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.09
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000067999

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:31.20

 All tests were passed




Server wird beendet - Lösche Semaphor 62259217.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.41
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.11
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.45
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.43
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.95
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6821.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.81
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45727
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869727
  j =  1                              :        399908551
  j =  2                              :            45717
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45864
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869864
  j =  1                              :        399908274
  j =  2                              :            45860
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.09e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.26e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.34e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.58
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   56.29
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.83
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.16
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.92
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.76
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.79
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  108.75
p-value of test                       :  5.3e-3


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.99
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.13
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.73
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.14
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.37
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.53
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.84
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.67
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3962.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.84
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.93
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.12
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.06
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000049198

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.42
p-value of test                       :  3.3e-3


-----------------------------------------------
Total number of bits:  7999946331

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:30.63

 All tests were passed




Server wird beendet - Lösche Semaphor 42532882.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5251
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.37
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.61
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4950.73
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908362
  j =  2                              :            45810
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907686
  j =  2                              :            46154
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.68e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.38
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.79
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.72
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   13.84
p-value of test                       :    0.9995    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.63
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.63
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.72
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.18
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.84
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.44
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.01
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.83
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.03
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.58
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  457.55
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.32
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.79
p-value of test                       :    0.9969


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.03
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.25
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3979.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.39
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.58
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999847925

Normal statistic for number of bits   :   -1.20
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.14
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000093124

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:05.73
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 75  RandomWalk1 M (L=50, r=25)      0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43253783.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.91
p-value of test                       :  9.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     110
p-value of test                       :    0.9996    *****

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.10
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1291.79
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:02:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.62
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.1e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.08
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.09
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.22
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908350
  j =  2                              :            45819
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908383
  j =  2                              :            45801
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    4.76
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.32
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.52
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.53
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.80
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.06
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.36
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.05
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.48
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.12
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.83
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.94
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.06
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.00
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.76
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.040
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.02
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11581.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.81
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000086278

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.32
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000026704

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:13.75
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NJumps, t = 16       0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44498967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:41.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.83
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6918.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.40
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908610
  j =  2                              :            45689
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46043
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870043
  j =  1                              :        399907919
  j =  2                              :            46033
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:30.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.78
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.69
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.69
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.10
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  180.63
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.37
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.44
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.74
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.75
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.70
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.48
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.56
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.22e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.47
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.43
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.71
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:20.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4879.05
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4685.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.10
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.10
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999885791

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.03
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999876512

Normal statistic for number of bits   :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:34.35

 All tests were passed




Server wird beendet - Lösche Semaphor 45809687.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5488
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4481
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.05
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    3.39
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.67
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  281.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.05
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-3
p-value of test                       :    0.9983

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.57
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.56
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5117.50
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:19.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45673
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869673
  j =  1                              :        399908655
  j =  2                              :            45671
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46088
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870088
  j =  1                              :        399907826
  j =  2                              :            46084
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9948


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.92e-6
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17760.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.24
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.24
p-value of test                       :  2.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.96
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.32
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.03
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.76
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.65
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.72
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.24
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.74
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.20
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.69
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.62
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.25
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.68
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4766.02
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11488.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.40
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999978260

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.80
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000029506

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:47.73

 All tests were passed




Server wird beendet - Lösche Semaphor 46759959.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5334
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    3.60
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.81
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7142.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.15
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.05
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45459
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869459
  j =  1                              :        399909088
  j =  2                              :            45447
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45600
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869600
  j =  1                              :        399908802
  j =  2                              :            45596
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.66e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17311.06
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.87
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.51
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.11
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.72
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.00
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.67
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.57
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.73
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.81
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.26
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.28
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.57
p-value of test                       :    0.9900


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.50
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.97
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.73
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.54
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.12
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3937.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.96
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999984440

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.82
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000041704

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:01.12

 All tests were passed




Server wird beendet - Lösche Semaphor 47742999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    2.27
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.22
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.59
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6832.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.01
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.08
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.14
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:55.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908016
  j =  2                              :            45983
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46186
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870186
  j =  1                              :        399907631
  j =  2                              :            46180
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.9931

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.33
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.17
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.92
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.05
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.11
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.10
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.01
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.50
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.52
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.44
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.33
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.80
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.52
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.79
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.22
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.33
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.22
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.54e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.08e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.09
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.19
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.32
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.97
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000030037

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000144118

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 2.26e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    5.75
p-value of test                       :  1.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.34
p-value of test                       :    0.9996    *****

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.97
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 106  AutoCor, d=3, r=27              0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48693271.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    3.12
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     181
p-value of test                       :  7.6e-3

Stat. AD (mNP2)                       :    4.80
p-value of test                       :  3.6e-3

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.11
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.38
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.79
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    3.65
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.70
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.22
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.59
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:16.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46294
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870294
  j =  1                              :        399907413
  j =  2                              :            46292
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46331
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870331
  j =  1                              :        399907341
  j =  2                              :            46325
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.92
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.11
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.08
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17780.13
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.04
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.36
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.59
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.51
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.79
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.05
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   90.43
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.64
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.39
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.81
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.22
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.36
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:34.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.33
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.01
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.82e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.44
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.00
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11558.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.46
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999854465

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.11
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999885737

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         : -8.58e-3
p-value of test                       :    0.50

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:07.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49643543.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.90
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.79
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.84
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7027.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.36
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.63
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.95
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:59.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907796
  j =  2                              :            46099
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908488
  j =  2                              :            45753
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.27
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.26
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17673.01
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.02
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.84
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.75
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.44
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.27
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.11
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.76
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.44
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.97
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5127.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.49
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.54
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.33
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.00
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.45
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999956726

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.82
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000039205

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.41

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:57.29

 All tests were passed




Server wird beendet - Lösche Semaphor 50561047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1249
p-value of test                       :    0.9992    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334369
  j =  1                              :        599997502
  j =  2                              :             1249
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.60
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.50
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.19
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.01
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:22.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.08
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.57
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.64
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45845
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869845
  j =  1                              :        399908312
  j =  2                              :            45841
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46039
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870039
  j =  1                              :        399907922
  j =  2                              :            46039
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.37e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.32e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.85
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.82
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17343.89
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.82
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.78
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.37
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.50
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.06
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.12
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.29
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.67
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5213.67
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.29
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.48
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.36
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.83
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10221.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.042
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.77
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.95
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999887354

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.67
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999915092

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.9905

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:55.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  8  CollisionOver, t = 7            0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51609623.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:52.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:41.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.23
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1357.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7134.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.72
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.71
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.30
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4914.83
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45602
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869602
  j =  1                              :        399908800
  j =  2                              :            45594
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907798
  j =  2                              :            46098
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.21e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.86
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.69
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.71
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.70
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.18
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.14
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.59
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.26
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.34
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  544.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.46
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.77
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.11
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.30
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.19
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.20
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.47e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.08
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:15.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4092.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.64
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000072007

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.90
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000031333

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:50.27

 All tests were passed




Server wird beendet - Lösche Semaphor 53149719.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5268
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    2.96
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9930

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.32
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907586
  j =  2                              :            46201
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908296
  j =  2                              :            45846
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:18.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.23e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 2.54e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.64
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.43
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17567.36
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.54
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.97
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.13
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.19
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.90
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.77
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4895.12
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.98
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.93
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5254.37
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.70
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.50
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.79
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.59e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.31e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.45
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4013.98
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.22
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.79
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000075664

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.91
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999983615

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:09.78

 All tests were passed




Server wird beendet - Lösche Semaphor 54067223.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9971

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7140.23
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  159.15
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4850.62
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907946
  j =  2                              :            46024
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908552
  j =  2                              :            45718
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.53e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.72e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.065
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.76
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.63
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.39
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.04
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.66
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.70
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.52
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.12
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.81
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4847.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.83
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.35
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.84
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    2.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-4
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  157.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9753.66
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.077
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:21.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.80
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.04
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000129715

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999843293

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Tests on the sum of all N observations
Standardized normal statistic         :   0.077
p-value of test                       :    0.47

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:19.54

 All tests were passed




Server wird beendet - Lösche Semaphor 55115799.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5269
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.17
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6937.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.92
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.02
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.36
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908144
  j =  2                              :            45922
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907899
  j =  2                              :            46043
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9935


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:30.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.97e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.66e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.75
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17633.45
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.90
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.90
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.16
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.48
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.10
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.88
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.54
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.33
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.09
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.26
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.63
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.61
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5115.66
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.75
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.65
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.08
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:19.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4269.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11638.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12152.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.07
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999945896

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.64
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000045931

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:28.12

 All tests were passed




Server wird beendet - Lösche Semaphor 56131607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5321
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.24
p-value of test                       :  2.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9990    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.70
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46323
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870323
  j =  1                              :        399907357
  j =  2                              :            46317
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908081
  j =  2                              :            45952
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  2.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-3
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.82
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.29
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17093.68
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  568.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.85
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.23
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.82
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.34
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.07
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.81
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.61
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.08
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.98
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.98
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.96
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    3.98
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  148.07
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9827.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:16.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    5.47
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4695.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.55
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999935042

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.24
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999923219

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.074
p-value of test                       :    0.53

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    2.54
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57180183.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9901

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:47.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.93
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.83
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:35.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.59
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46035
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870035
  j =  1                              :        399907931
  j =  2                              :            46033
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907847
  j =  2                              :            46066
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.12
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.13
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.03
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.43
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.87
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.87
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.75
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5164.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.70
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.66
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.26
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.40
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.71
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.09
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -2.29
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.39
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.55
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.71
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999995435

Normal statistic for number of bits   :  -0.036
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.21
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999926192

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.18
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:44.19

 All tests were passed




Server wird beendet - Lösche Semaphor 58195991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    3.25
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.72
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.77
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.56
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.19
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908292
  j =  2                              :            45848
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908381
  j =  2                              :            45808
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.70e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.10
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.29
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.07
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.84
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.85
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.72
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.15
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.28
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.63
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.71
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.62
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.11
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000016420

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.04
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000073933

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:48.07

 All tests were passed




Server wird beendet - Lösche Semaphor 59211799.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:41.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.57
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.70
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.17
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.37
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907409
  j =  2                              :            46294
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908469
  j =  2                              :            45758
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -2.85e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.81
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17209.77
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.56
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.46
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.70
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.20
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.96
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.83
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.74
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.55
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.28
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.91
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.33
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.22
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.22
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.91
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.43
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   0.070
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.55e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.00
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.47
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999964331

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.53
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000064129

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.21
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:46.44

 All tests were passed




Server wird beendet - Lösche Semaphor 60227607.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5313
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7165
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  247.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.00
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.56
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908344
  j =  2                              :            45825
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908112
  j =  2                              :            45935
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.17e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17349.41
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.91
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.79
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.91
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.88
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.33
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.30
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.65
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.88
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.13
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.45
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.49
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.18e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.59
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12012.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.65
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000092929

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.24
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000065353

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.22

 All tests were passed




Server wird beendet - Lösche Semaphor 61243415.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.76
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:25.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.20
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.40
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908196
  j =  2                              :            45896
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908082
  j =  2                              :            45956
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.90e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 3.46e-4
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.075
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.95
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.53
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.26
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.53
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.14
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.25
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.46
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.31
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.81
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.83
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.07
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.95
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.12
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.44
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10052.46
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.66
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.26
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999836351

Normal statistic for number of bits   :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.49
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999990320

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Tests on the sum of all N observations
Standardized normal statistic         : 2.56e-3
p-value of test                       :    0.50

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:18.12

 All tests were passed




Server wird beendet - Lösche Semaphor 62226455.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.22
p-value of test                       :  2.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5106.44
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907896
  j =  2                              :            46049
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46053
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870053
  j =  1                              :        399907898
  j =  2                              :            46045
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 9.36e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.66e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.58e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.07
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.72
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.68
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.98
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.95
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.86
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.51
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.61
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4876.48
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.80
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.64
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.85
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.44
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.52
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.65
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.06
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5104.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999939851

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.32
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999975107

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.15
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:25:21.90

 All tests were passed




Server wird beendet - Lösche Semaphor 42565651.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:38.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.83
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   85.13
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.13
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.41
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.04
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:17.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.66
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.00
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.36
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908877
  j =  2                              :            45554
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908480
  j =  2                              :            45751
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.46e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.23e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.90
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.42
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:19.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17316.34
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.11
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.82
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.95
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.17
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.83
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.48
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.18
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.82
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.53e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.84
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.40
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.31
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5015.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.93
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12089.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.28
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000007417

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.45
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999983192

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:05.56

 All tests were passed




Server wird beendet - Lösche Semaphor 43941907.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.62
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     657
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.73
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.12
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.95
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:55.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908631
  j =  2                              :            45680
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908227
  j =  2                              :            45879
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.08e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.11
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17366.16
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.65
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.94
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.18
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.22
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.89
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.22
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.66
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.48
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.13
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.67
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.14
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.31
p-value of test                       :    0.9930


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.56
p-value of test                       :    0.9948

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.02
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4684.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11654.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.44
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000013840

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.12
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000016723

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   0.046
p-value of test                       :    0.48

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:36.20

 All tests were passed




Server wird beendet - Lösche Semaphor 44957715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7001.01
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.53
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.77
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.88
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:47.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.60
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.11
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907672
  j =  2                              :            46158
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.26
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.56
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.49
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.56
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.57
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.05
p-value of test                       :  4.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.75
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4819.43
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4961.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.05
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -1.57
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.24e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11960.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.00
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999904775

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.27
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999934880

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:46.29

 All tests were passed




Server wird beendet - Lösche Semaphor 45875219.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5369
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.94
p-value of test                       :  9.5e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.35
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.89
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.87
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908203
  j =  2                              :            45897
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.55e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.81
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.00
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.67
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.02
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.22
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.45
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.11
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.22
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.60
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.22
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.40
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.15
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12051.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11489.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.48
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000094606

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.86
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999868997

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:34.64

 All tests were passed




Server wird beendet - Lösche Semaphor 47120403.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1270
p-value of test                       :    0.9948

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334390
  j =  1                              :        599997460
  j =  2                              :             1270
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4445
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    5.06
p-value of test                       :  2.7e-3

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.87
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908379
  j =  2                              :            45809
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.80e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      : -1.46e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.33e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16979.88
p-value of test                       :    0.9924



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.19
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.29
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.18
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.32
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.10
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.42
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.45
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.38
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.72
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.37
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.67
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.57
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.96
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5123.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.90
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.19
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.84
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.17e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 4.09e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.78
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.02e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.19
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.35
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11718.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.30
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999996458

Normal statistic for number of bits   :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.92
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999958004

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:42.10

 All tests were passed




Server wird beendet - Lösche Semaphor 48136211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:50.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    3.34
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.04
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1496.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7175.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.50
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.27
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.94
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908711
  j =  2                              :            45640
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46199
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870199
  j =  1                              :        399907602
  j =  2                              :            46199
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.12e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.70e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.59e-3
p-value of test                       :    0.9984

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16915.88
p-value of test                       :    0.9973



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.57
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.19
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.08
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.68
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.76
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.75
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.80
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.74
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.74
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.94
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.38
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.98
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.62
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.05
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.28
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4839.85
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12092.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.80
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000012847

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.43
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999919910

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.041
p-value of test                       :    0.48

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:46.42

 All tests were passed




Server wird beendet - Lösche Semaphor 49119251.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.08
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7248.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:31.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:47.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.17
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.25
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908115
  j =  2                              :            45938
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46149
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870149
  j =  1                              :        399907708
  j =  2                              :            46137
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.28
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.07e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.93
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.99
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.3e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17924.28
p-value of test                       :  4.3e-3



-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.06
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.20
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.52
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.56
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.70
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.17
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.04
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  313.74
p-value of test                       :    0.9964


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.12
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.76
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.91
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9939.54
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.10
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.89
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.40
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12122.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.95
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999855437

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.98
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999986369

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:29.50

 All tests were passed




Server wird beendet - Lösche Semaphor 50266131.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:11.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.83
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.13
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.09
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6999.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.69
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.36
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.25
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5065.89
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45550
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869550
  j =  1                              :        399908905
  j =  2                              :            45540
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908105
  j =  2                              :            45946
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.38e-4
p-value of test                       :  4.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 5.91e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    5.75
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.90
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.38
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.48
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.46
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.68
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.41
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.91
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.11
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.08
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.91
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.67
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.78
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.42
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.96
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:34.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.90
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.50
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12113.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.41
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.80
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000049969

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.17
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000077050

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:19.67

 All tests were passed




Server wird beendet - Lösche Semaphor 51380243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.44
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1314.28
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:07.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.80
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.27
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908061
  j =  2                              :            45968
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908705
  j =  2                              :            45637
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.34
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.87
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.77
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.14
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.54
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.93
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.47
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.10
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.88
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5138.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.09
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.81
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.58
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4995.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3939.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12168.85
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.08
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000165916

Normal statistic for number of bits   :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.28
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999842183

Normal statistic for number of bits   :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.54

 All tests were passed




Server wird beendet - Lösche Semaphor 52396051.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9986

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.76
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.14
p-value of test                       :    0.9991    *****

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.27
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.91
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.32
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.35
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.47
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.41
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.78
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:01.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46048
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870048
  j =  1                              :        399907909
  j =  2                              :            46038
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45540
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869540
  j =  1                              :        399908924
  j =  2                              :            45532
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.42
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.16
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  178.17
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.16
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.18
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.62
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.51
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.30
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.99
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.58
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.17
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.85
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.05
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.44
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.31
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4803.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.29
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.99
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.68
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10256.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.18
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.79
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000027241

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.99
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000066898

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:07.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53444627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:11.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.03
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.13
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6852.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.44
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.83
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.40
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5209.01
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45462
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869462
  j =  1                              :        399909081
  j =  2                              :            45452
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45767
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869767
  j =  1                              :        399908470
  j =  2                              :            45759
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   17.78
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17407.27
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.45
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.13
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.41
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.88
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.16
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.10
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.71
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.60
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.23
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.06
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.14
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000198535

Normal statistic for number of bits   :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.77
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000145309

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:25.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54460435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.10
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7319.03
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.99
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.41
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.34
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.18
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.41
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45474
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869474
  j =  1                              :        399909057
  j =  2                              :            45464
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908139
  j =  2                              :            45926
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-5
p-value of test                       : 1 -  6.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.11e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.02
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.94
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.72
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.92
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.34
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.31
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.13
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.22
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.96
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5120.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.20
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:13.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10234.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.98
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.91
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000059662

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.44
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000062692

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.70
p-value of test                       :    0.04

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:42.45

 All tests were passed




Server wird beendet - Lösche Semaphor 55509011.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5555
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7521
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.83
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     351
p-value of test                       :  2.2e-3

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.22
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1437.16
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7237.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.71
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:02.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45685
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869685
  j =  1                              :        399908636
  j =  2                              :            45673
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908643
  j =  2                              :            45677
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9907


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.12e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.99
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.27
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17360.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.38
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.13
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.69
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.60
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.95
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.19
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:19.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    2.05
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.67e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.32e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.96
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:15.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.97
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000041860

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.76
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999923519

Normal statistic for number of bits   :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:37.69

 All tests were passed




Server wird beendet - Lösche Semaphor 56557587.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.85
p-value of test                       :  3.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.45
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.40
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.99
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7221.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.10
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.53
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4944.62
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:04.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908319
  j =  2                              :            45836
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907751
  j =  2                              :            46117
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17645.43
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.98
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.77
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.42
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.83
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.58
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.45
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.80
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4792.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.45
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.75
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.52
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.28
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.65
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:10.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.76
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:52.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3903.86
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.14
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.91
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000027226

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.68
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000052666

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:59.25

 All tests were passed




Server wird beendet - Lösche Semaphor 57606163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7111
p-value of test                       :    0.9924


-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.42
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.40
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6954.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.08
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.91
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908477
  j =  2                              :            45751
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.33e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.46e-5
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    4.50
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.65e-4
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.12
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:51.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   21.63
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.79
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.42
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.11
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.33
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.59
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.81
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.59
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.55
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.38
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  258.37
p-value of test                       :  3.4e-3


-----------------------------------------------
CPU time used                    :  00:00:34.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.28
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.09
p-value of test                       :    0.9949


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.65
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.59e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10297.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12059.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.97
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000108331

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.34
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999920135

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    3.60
p-value of test                       :  1.7e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.6e-3

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:47.50

 All tests were passed




Server wird beendet - Lösche Semaphor 58654739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.81
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7090.88
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.86
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.23
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.64
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.18
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908348
  j =  2                              :            45817
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45279
p-value of test                       :    0.9975


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869279
  j =  1                              :        399909445
  j =  2                              :            45273
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.8e-3

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9950


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.71e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.46
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.42
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.96
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.10
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.00
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.19
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.05
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.98
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.95
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.06
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.49
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.03
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.25
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.99
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.44
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.67
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.74
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.13
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.07e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.05
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.22e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.19
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.23
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.35
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.06
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999984089

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000083275

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:32.63

 All tests were passed




Server wird beendet - Lösche Semaphor 59703315.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.90
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.57
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.92
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4886.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908154
  j =  2                              :            45914
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908450
  j =  2                              :            45769
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.54e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    4.22
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17967.54
p-value of test                       :  2.2e-3



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.36
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.87
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.85
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.42
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.06
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.08
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.51
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.08
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.92
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.21
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.90
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.09
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.15
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.79
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.41
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.11
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.05
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999972398

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.35
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000079156

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.38
p-value of test                       :  8.7e-3

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:54.50

 All tests were passed




Server wird beendet - Lösche Semaphor 60751891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4460
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:05:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.25
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.42
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.36
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.62
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907899
  j =  2                              :            46046
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908179
  j =  2                              :            45909
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.82
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.93
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.31
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.07
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.90
p-value of test                       :  4.7e-3


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.15
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.83
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.28
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.21
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.34
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.51
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.58
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.73
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.59
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.69
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.91e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.28
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.45
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.01
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000019777

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000127522

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:11.26

 All tests were passed




Server wird beendet - Lösche Semaphor 61800467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997319
  j =  2                              :             1339
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4223
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.07
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.01
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:09.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.49
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.06
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45794
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869794
  j =  1                              :        399908415
  j =  2                              :            45788
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907758
  j =  2                              :            46118
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 9.38e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.79e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.051
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.28
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.61
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.66
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.46
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.18
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.31
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.62
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:34.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.65
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.60
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.00
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.43
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.71
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.75
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.69
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.56
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:11.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.11
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.07
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.63
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9996.50
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:20.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5046.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.60
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999892859

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.37
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000097840

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.37e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:00:38.05

 All tests were passed




Server wird beendet - Lösche Semaphor 62816275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:00.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.78
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:47.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.41
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.05
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.27
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.23
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908577
  j =  2                              :            45707
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45611
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869611
  j =  1                              :        399908783
  j =  2                              :            45601
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.18e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.20e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.67e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.38
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.89
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17453.06
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.67
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.08
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.66
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.09
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.51
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.32
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.75
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.24
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.85e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:33.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.37
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.83
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:33.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.51
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11888.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.80
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999907883

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.54
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999970892

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.76
p-value of test                       :    0.96

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:23:49.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42598420.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:00:58.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.46
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     648
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.16
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.66
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.92
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.20
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9967


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908644
  j =  2                              :            45675
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45244
p-value of test                       :    0.9985


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869244
  j =  1                              :        399909514
  j =  2                              :            45240
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.80
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.22
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17282.25
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.93
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.98
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.40
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.63
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  418.76
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.03
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.06
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.30
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.29
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.43
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.97
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.93
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9923

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.51
p-value of test                       :    0.9925

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.27
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.29
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.44
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  8000068929

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.76
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000047644

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:22.18

 All tests were passed




Server wird beendet - Lösche Semaphor 43974676.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    2.37
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.13
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4929.53
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908019
  j =  2                              :            45986
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908199
  j =  2                              :            45896
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:28.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.99e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.93
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.28
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17258.66
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.97
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.60
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.16
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.06
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.95
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.59
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.47
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.34
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.13
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.62
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.44
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.50e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.14
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10360.49
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.9e-4    *****

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5111.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.03
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000004798

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.88
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000081961

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.19
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:30.20

 All tests were passed




Server wird beendet - Lösche Semaphor 44990484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7070
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:04:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    3.46
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.44
p-value of test                       :  5.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.97
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.75
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.97
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7144.16
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.59
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.35
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.60
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45483
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869483
  j =  1                              :        399909034
  j =  2                              :            45483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907890
  j =  2                              :            46052
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.94e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.78
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.77
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.78
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.39
p-value of test                       :  9.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.32
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.87
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.26
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.60
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.03
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.08
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.56
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.11
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.25
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.55
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5131.46
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.88
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -1.88
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.59
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.98
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.76
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.01
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9822.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3958.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11612.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.22
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999929693

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.28
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999917348

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:35.67

 All tests were passed




Server wird beendet - Lösche Semaphor 45973524.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.83
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.17
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.52
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  162.35
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908367
  j =  2                              :            45812
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908625
  j =  2                              :            45683
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
p-value of test                       :    0.9981

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :  4.2e-3

Anderson-Darling statistic = A2       :    4.29
p-value of test                       :  6.4e-3


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-5
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    : 3.35e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.73
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.5e-3

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.96
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.09
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.18
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.85
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.34
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.09
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.79
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.05
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.67
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.34
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.17
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.07
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.71
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:19.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4263.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11624.41
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.06
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000048109

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000043816

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:40.28

 All tests were passed




Server wird beendet - Lösche Semaphor 46923796.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:12.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     983
p-value of test                       :  3.3e-3

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:43.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.93
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.78
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4878.41
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:54.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908527
  j =  2                              :            45729
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907831
  j =  2                              :            46083
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.55
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.46
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.31
p-value of test                       :  6.4e-3

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17717.15
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.99
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.44
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.29
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.93
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.73
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.01
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.39
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.18
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.02
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.48
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.61
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.01
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.07
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 4.24e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.10
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.84
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999946637

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.16
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999946376

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.012
p-value of test                       :    0.50

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:28.63

 All tests were passed




Server wird beendet - Lösche Semaphor 47874068.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5445
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.08
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  508.35
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6757.11
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.78
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.15
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.00
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.79
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:14.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908534
  j =  2                              :            45727
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908462
  j =  2                              :            45763
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:33.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.32e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17493.46
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.86
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.54
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.98
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.98
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.01
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.39
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.90
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.13e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.31
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:29.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.38
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000099871

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.91
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999930641

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:18.81

 All tests were passed




Server wird beendet - Lösche Semaphor 49184788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.72
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.52
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.46
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.97
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.56
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:54.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908371
  j =  2                              :            45810
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908705
  j =  2                              :            45640
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.66
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.40
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.50
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.24
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.60
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.21
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.70
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.75
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.26
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.75
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.59
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.86
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.18e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.28
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.97
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10316.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11499.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11871.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.38
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999867683

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.74
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999854168

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 6.81e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:31.43

 All tests were passed




Server wird beendet - Lösche Semaphor 50233364.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.62
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.03
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45805
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869805
  j =  1                              :        399908392
  j =  2                              :            45801
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907853
  j =  2                              :            46069
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.92e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.55
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.70
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.49
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17128.41
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.14
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.86
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.91
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.77
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.63
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.12
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.66
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.41
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.60
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.20
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.66
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.04e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.97
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.13
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.38
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.77
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.68
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11627.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.50
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000075511

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.81
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000011665

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:54.81

 All tests were passed




Server wird beendet - Lösche Semaphor 51281940.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.91

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:09.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.69
p-value of test                       :  4.1e-3

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.37
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.82
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.47
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.77
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.85
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5167.72
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45684
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869684
  j =  1                              :        399908633
  j =  2                              :            45682
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908609
  j =  2                              :            45685
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.63e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.74
p-value of test                       :  3.1e-3

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.55
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.30
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.45
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17113.20
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.94
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.63
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.09
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.17
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.51
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.61
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.56
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.34
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.25
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.62
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.14
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.21
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.08
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999932507

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.92
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999986828

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:53.64

 All tests were passed




Server wird beendet - Lösche Semaphor 52330516.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7174
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.97
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.72
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46160
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870160
  j =  1                              :        399907685
  j =  2                              :            46150
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45548
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869548
  j =  1                              :        399908912
  j =  2                              :            45532
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.12e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17346.99
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.08
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.82
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.71
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.67
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.26
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.24
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.79
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.42
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.73
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.09
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.26
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.18
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.55
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.35
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.04
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000053374

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.69
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000103048

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         : -1.62e-3
p-value of test                       :    0.50

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.07

 All tests were passed




Server wird beendet - Lösche Semaphor 53346324.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     845
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.16
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.89
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1317.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.28
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.09
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.17
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9960


-----------------------------------------------
CPU time used                    :  00:02:59.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45934
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869934
  j =  1                              :        399908136
  j =  2                              :            45926
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908508
  j =  2                              :            45740
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:31.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.75
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.37e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.91e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.30e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.64
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.64
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.25
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.61
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.15
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.05
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.68
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.23
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.19
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.80
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.99
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.04
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.04
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.74
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.65
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.36
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.37
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.88
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.86
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.87
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.74e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.00
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.16
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.14
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.04e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10317.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9708.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12013.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.97
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000173773

Normal statistic for number of bits   :    1.37
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.14
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999938624

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.06

 All tests were passed




Server wird beendet - Lösche Semaphor 54362132.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4242
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.47
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.99
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.89
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.06
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45715
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869715
  j =  1                              :        399908574
  j =  2                              :            45707
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908253
  j =  2                              :            45869
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.08e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.53e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.10
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.51
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:42.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17755.48
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.65
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.42
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.83
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.92
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.17
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.46
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.45
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.14
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.88
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.47
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.13
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 4.64e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.45
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10059.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:29.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4914.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4313.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.50
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999886235

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.69
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999955754

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.067
p-value of test                       :    0.53

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.56
p-value of test                       :    0.94

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:42.88

 All tests were passed




Server wird beendet - Lösche Semaphor 55410708.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    4.70
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.42
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.83
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.03
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.54
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.62
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.74
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.10
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45706
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869706
  j =  1                              :        399908593
  j =  2                              :            45696
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907881
  j =  2                              :            46055
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.90e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.50
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.03
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.04
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.69
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.50
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.28
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.56
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.47
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  105.37
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.78
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.79
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.23
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.32
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.52
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.44
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.15
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         : 5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.85
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.75
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10245.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:00.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4293.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11956.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.71
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000031906

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.06
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999919493

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:55.04

 All tests were passed




Server wird beendet - Lösche Semaphor 56524820.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5284
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.50
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7146.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5151.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:01.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908110
  j =  2                              :            45942
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908645
  j =  2                              :            45673
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.86e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.18e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.14
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.66
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.39
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.13
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.81
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.57
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.10
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.37
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.86
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.70
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.32
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.03
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.42
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.60
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.96e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.49
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.48e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:12.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.79
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.38
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.28
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999962495

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.50
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000052867

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:19.85

 All tests were passed




Server wird beendet - Lösche Semaphor 57573396.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:48.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.61
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.91
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:25.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.62
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.84
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.41
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45375
p-value of test                       :    0.9908


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869375
  j =  1                              :        399909252
  j =  2                              :            45371
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45844
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869844
  j =  1                              :        399908315
  j =  2                              :            45838
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:33.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.23
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.19
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.68
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  104.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17251.71
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.20
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.39
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.35
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.82
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.60
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  454.75
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.64
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.91
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.65e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.04
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.091
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4705.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11862.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.55
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999869414

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.18
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999933155

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:37.40

 All tests were passed




Server wird beendet - Lösche Semaphor 58556436.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7470
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     951
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.98
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.91
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.67e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.86
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :  100.92
p-value of test                       :  7.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.58
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.75
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4965.08
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:56.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45614
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869614
  j =  1                              :        399908773
  j =  2                              :            45612
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45438
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869438
  j =  1                              :        399909127
  j =  2                              :            45432
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.38
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.32
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.47
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.01
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.94
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.01
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.17
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.27
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.76
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.02
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  312.70
p-value of test                       :    0.9938


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.07
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.41
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.43
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.41
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    1.51
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.59
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.62
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.037
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4700.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.34
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.77
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999959240

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.78
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999930464

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:04.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 39  Run, r = 15                     7.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59670548.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9906

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907456
  j =  2                              :            46266
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908416
  j =  2                              :            45780
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.67
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.18
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.46
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.38
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.83
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.76
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.76
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.16
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.55
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  472.29
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.93
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  157.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.58
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.78
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.64
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.31
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.48
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.85e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4604.77
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.22
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000099913

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.23
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000130246

Normal statistic for number of bits   :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    2.93
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:19.27

 All tests were passed




Server wird beendet - Lösche Semaphor 60686356.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4468
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     545
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.42
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.83
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.73
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5119.21
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907700
  j =  2                              :            46150
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907964
  j =  2                              :            46012
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.39e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.21e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.38
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.88
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.79
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.68
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.32
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.04
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.61
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.45
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  101.67
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.65
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.47
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4857.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.75
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.99
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.60
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    2.30
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.49
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.52
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:13.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11768.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.59
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999797348

Normal statistic for number of bits   :   -1.60
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.66
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000059917

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:40.90

 All tests were passed




Server wird beendet - Lösche Semaphor 61702164.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5473
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.96
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     120
p-value of test                       :    0.9934

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.72
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.99
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7340.40
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.80
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.32
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.78
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4835.95
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908119
  j =  2                              :            45930
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907959
  j =  2                              :            46016
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:33.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.100
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.03
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.58
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   69.60
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.46
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17164.12
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.40
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.41
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.36
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.29
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.62
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.16
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:33.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.27
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4850.00
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.45
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:33.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.11e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.99
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.95
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3940.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11853.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.95
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999916988

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   93.04
p-value of test                       :  7.6e-4    *****


-----------------------------------------------
Total number of bits:  8000242839

Normal statistic for number of bits   :    1.92
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:54.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             7.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62717972.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.26
p-value of test                       :  2.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    3.55
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    5.30
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.38
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.23
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.72
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908229
  j =  2                              :            45884
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45266
p-value of test                       :    0.9979


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869266
  j =  1                              :        399909469
  j =  2                              :            45264
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.74
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.71
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17520.20
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.31
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.30
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.88
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4875.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.24
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.92
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.70
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.41
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :  -0.095
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   30.56
p-value of test                       :  2.3e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.46
p-value of test                       :    0.9931



-----------------------------------------------
CPU time used                    :  00:02:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10109.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10187.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4757.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.60
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999969710

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.74
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999962906

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:32.45

 All tests were passed




Server wird beendet - Lösche Semaphor 42631189.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    5.33
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.62
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:10.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.68
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.19
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46205
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870205
  j =  1                              :        399907596
  j =  2                              :            46193
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46326
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870326
  j =  1                              :        399907351
  j =  2                              :            46320
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:32.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17638.44
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.73
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.72
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.30
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.12
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.33
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.51
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.62
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  463.58
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.54
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.53e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.11
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.89
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.29
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.72
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9707.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:34.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4734.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12115.40
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.56
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000170602

Normal statistic for number of bits   :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.49
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999976622

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.056
p-value of test                       :    0.48

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:54.82

 All tests were passed




Server wird beendet - Lösche Semaphor 43614229.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.09
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.96
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  395.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.58
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.48
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.06
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45333
p-value of test                       :    0.9947


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869333
  j =  1                              :        399909336
  j =  2                              :            45329
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:32.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:20.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  4.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.10e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.54
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.27
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.19
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.42
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.26
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.06
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.53
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.94
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.24
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.95
p-value of test                       :  1.6e-3

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 7.65e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.00e-2
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.27
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10273.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:33.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.69
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000035233

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.42
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000089263

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:54.18

 All tests were passed




Server wird beendet - Lösche Semaphor 44826645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4486
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.12
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.87
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.34
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   91.28
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.97
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4718.12
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908312
  j =  2                              :            45838
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908473
  j =  2                              :            45762
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.06
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.07
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.35
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.09
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.40
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.12
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.73
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.89
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.65
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.34
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.40
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.73
p-value of test                       :  6.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.30
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.79
p-value of test                       :  5.9e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    3.06
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.53
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.50
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.76
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.40
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000066556

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.65
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999956261

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:30.76
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45940757.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5293
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.19
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.74
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7076.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.78
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.18
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907785
  j =  2                              :            46100
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.21e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.05
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17340.25
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.70
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.09
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.41
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.92
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.38
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.77
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.48
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.45
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.60
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.58
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.79
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    2.41
p-value of test                       :  7.9e-3



-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.45
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.01e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.07
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9717.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.26
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:32.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.32
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12182.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11977.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.94
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000038509

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.27
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000042448

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:30.43

 All tests were passed




Server wird beendet - Lösche Semaphor 47022101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.22
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1507.36
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.95
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.78
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.16
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:56.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46189
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870189
  j =  1                              :        399907624
  j =  2                              :            46185
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908728
  j =  2                              :            45633
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.3e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9963


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.19e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.58e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.029
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.72
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.42
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.76
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.95
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.17
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.82
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.18
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.27
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.62
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.88
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.99
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.38
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.50
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.38
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.62
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.86
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.06
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.52e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.10
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.86
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:20.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.11
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.88e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4666.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3935.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11645.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12095.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.84
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000103333

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.67
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000058210

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:08.48

 All tests were passed




Server wird beendet - Lösche Semaphor 48103445.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9965

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  363.19
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1442.06
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7205.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.72
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.12
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45519
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869519
  j =  1                              :        399908963
  j =  2                              :            45517
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907555
  j =  2                              :            46215
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-5
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    : 2.79e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.020
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.26
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17677.22
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.16
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.49
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.15
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.94
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.84
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.91
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.29
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.46
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.38
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.06
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.87
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.18
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.07
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.82e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.21
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   23.77
p-value of test                       :  2.5e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.099
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.70
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999997529

Normal statistic for number of bits   :  -0.020
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.60
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000007351

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.14

 All tests were passed




Server wird beendet - Lösche Semaphor 49020949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.83
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.01
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  274.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7139.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.27
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.84
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.11
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46275
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870275
  j =  1                              :        399907454
  j =  2                              :            46267
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908458
  j =  2                              :            45765
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.56e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.47
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17250.77
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.00
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.23
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.53
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.42
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.09
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.81
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.32
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.26
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.77
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.05
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.02
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.20
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.04
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.26e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.84
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.74
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11506.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.84
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999879884

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.76
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999939479

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.20
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:43.22

 All tests were passed




Server wird beendet - Lösche Semaphor 49971221.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5291
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.86
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.07
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.75
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907879
  j =  2                              :            46056
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908394
  j =  2                              :            45800
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.09e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.17
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.14
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17676.64
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.84
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.77
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.39
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.94
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.02
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.36
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.23
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.87
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.28
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.80
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.08
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.48
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.50
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -2.09
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.44e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.10
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4151.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.64
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999927491

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.82
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000020125

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:34.56

 All tests were passed




Server wird beendet - Lösche Semaphor 50987029.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997219
  j =  2                              :             1389
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1527
p-value of test                       :  8.0e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334647
  j =  1                              :        599996946
  j =  2                              :             1527
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.86
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.26
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.79
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1486.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.20
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.74
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:58.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45744
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869744
  j =  1                              :        399908520
  j =  2                              :            45728
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907760
  j =  2                              :            46111
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.77e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.23e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.03e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.21
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.18
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.92
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.89e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.93
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.38
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.35
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.01
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.40
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.97
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.74
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.78
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.37
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.60
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.15
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.95
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.13
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   27.41
p-value of test                       :  6.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.83
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.71
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.36
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.16
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.33
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000033121

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.90
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000137056

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           8.0e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51904533.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7566
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:03:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    3.49
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.99
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.43
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7212.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.10
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.52
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908451
  j =  2                              :            45770
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908344
  j =  2                              :            45822
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-4
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    : 9.49e-6
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.78
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17091.31
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.91
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.95
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.07
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.51
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.86
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.38
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.61
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.38
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.82
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.97
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.20
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  299.48
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.55
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.46
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.33
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.49e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.68
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.16
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10212.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.18
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.69
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000094912

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.69
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999951737

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.57
p-value of test                       :    0.06

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.062
p-value of test                       :    0.48

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.54

 All tests were passed




Server wird beendet - Lösche Semaphor 52854805.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.88
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.02
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.37
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6738.38
p-value of test                       :    0.9957

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.60
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908626
  j =  2                              :            45681
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908652
  j =  2                              :            45665
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.49
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.31
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17557.83
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.38
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.59
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.55
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.96
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.19
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.27
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.14
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.76
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.55
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.00
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.73
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.75
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.47
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    2.10
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.67
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.93
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.66
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10144.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4624.26
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.40
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000106765

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.25
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999883943

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:51.36

 All tests were passed




Server wird beendet - Lösche Semaphor 53837845.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.04
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.77
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.88
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.39
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.61
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.02
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.99
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.78
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:20.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.53e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.18
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17649.68
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.74
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.23
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.73
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.37
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.61
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.11
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.96
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.50
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.45
p-value of test                       :  1.0e-2


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.51
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  492.47
p-value of test                       :  6.5e-5    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.35
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.83
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.00e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.82
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.42
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9809.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.59
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.59
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999989663

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.55
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999976100

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.78

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:01.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   6.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54951957.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.50
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.06
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    1.84
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.96
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.41
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.67
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7167.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.31
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.79
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.45
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4962.86
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45702
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869702
  j =  1                              :        399908601
  j =  2                              :            45692
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907790
  j =  2                              :            46105
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980


-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.62
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17276.64
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.84
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.53
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.89
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.90
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.44
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.08
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.98
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.41
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.90
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.74
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.41
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.04
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.16
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.90e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.44
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4284.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.35
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000017875

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.61
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000087547

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.73

 All tests were passed




Server wird beendet - Lösche Semaphor 56066069.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.93
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.46
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.27
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4723.49
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:25.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45475
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869475
  j =  1                              :        399909054
  j =  2                              :            45467
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908479
  j =  2                              :            45756
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.31e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.54e-6
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.28
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.55
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.61
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.68
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.51
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.88
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.04
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.41
p-value of test                       :    0.9930


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.16
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.41
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.83
p-value of test                       :    0.9941


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.23e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.78
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.29
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.27
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000041296

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.88
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999971027

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:11.96
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 42  Permutation, t = 7              0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57114645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.87
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.74
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.52
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7093.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.86
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.67
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.30
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908110
  j =  2                              :            45939
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907945
  j =  2                              :            46020
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :  1.4e-3

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9975


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 6.99e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.32
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.45
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17388.61
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.95
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.65
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.28
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.76
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.33
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.43
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  214.24
p-value of test                       :  2.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.16
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.95
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.32
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.13
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.29
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.09
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.27
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.01
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.71
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.39
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:19.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.52e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.61
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11440.73
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11468.24
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.09
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999865151

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.47
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000054145

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    2.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58130453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7116
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     534
p-value of test                       :    0.9967

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    4.38
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:02:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.07
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.47
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  520.65
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908449
  j =  2                              :            45771
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46021
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870021
  j =  1                              :        399907961
  j =  2                              :            46015
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9955


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.17e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -9.65e-5
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.096
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17768.43
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.05
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.13
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.87
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.54
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.21
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.56
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  246.26
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.01
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.38
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   31.75
p-value of test                       :  1.5e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.24
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.70
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.083
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4651.97
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:52.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.62
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.83
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000015868

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.97
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000003622

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.097
p-value of test                       :    0.46

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:25.70

 All tests were passed




Server wird beendet - Lösche Semaphor 59080725.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5244
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:03:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.31
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     955
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.73
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.53
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.75
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.25
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:11.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.40
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5271.22
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:12.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45486
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869486
  j =  1                              :        399909031
  j =  2                              :            45480
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907657
  j =  2                              :            46170
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.9951

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.29e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.30e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.9915

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17684.30
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.75
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.51
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.46
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.74
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.38
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.96
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.74
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.16
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.94
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.68
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.21
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5081.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  453.80
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.52
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.43
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.52
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.82
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.37
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.92
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.78
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.39
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5111.83
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4413.87
p-value of test                       :  6.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11759.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.82
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000135058

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.89
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000097735

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:55.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       6.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60129301.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4482
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.19
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6892.86
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.14
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.67
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4812.42
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908099
  j =  2                              :            45946
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45729
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869729
  j =  1                              :        399908546
  j =  2                              :            45721
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 7.87e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.80
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17328.29
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.61
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.28
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.53
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.14
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.76
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.70
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  308.75
p-value of test                       :    0.9981


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.68
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.74
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.90e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.63e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10095.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.11
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.66
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11614.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12114.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.69
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999918014

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.72
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000055207

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:42.55

 All tests were passed




Server wird beendet - Lösche Semaphor 61112341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7507
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    3.58
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.94
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.22
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.13
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:09.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.95
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.18
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908369
  j =  2                              :            45811
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908295
  j =  2                              :            45851
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.61
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.78
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.94
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.28
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4869.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.23
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.38
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.27
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.85
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10198.56
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.69
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:13.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.98
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4963.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.68
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11828.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.02
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000023962

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.74
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999990164

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         : 4.04e-3
p-value of test                       :    0.50

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.45

 All tests were passed




Server wird beendet - Lösche Semaphor 62160917.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:34.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4183
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:00.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    4.19
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.50
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.25
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.46
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.07
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.47
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46363
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870363
  j =  1                              :        399907275
  j =  2                              :            46361
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46070
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870070
  j =  1                              :        399907863
  j =  2                              :            46064
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:32.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.19e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.23e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.047
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   36.95
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17471.21
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   49.38
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.87
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.78
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.62
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.81
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.99
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.74
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.70
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.62
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.24
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.68
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.44e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.59
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.32
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.03
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11597.82
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.43
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000083938

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.99
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000022306

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :  -0.050
p-value of test                       :    0.52

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:09.51

 All tests were passed




Server wird beendet - Lösche Semaphor 42663958.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9932

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:42.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.23
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.10
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7061.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.00
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.34
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.36
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907981
  j =  2                              :            46002
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907927
  j =  2                              :            46035
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:33.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931


-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.07
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   13.79
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17392.77
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.37
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.90
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.65
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.40
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.66
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.39
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.90
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.91
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.78
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.13
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:28.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.91
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.82
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.13
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.27
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000009079

Normal statistic for number of bits   :   0.072
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.38
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000241966

Normal statistic for number of bits   :    1.91
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:01.64

 All tests were passed




Server wird beendet - Lösche Semaphor 43384854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5332
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    3.58
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:10.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.95
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.17
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.29
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908557
  j =  2                              :            45720
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908301
  j =  2                              :            45848
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.87e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.44
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.54
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.45
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.45
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.83
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.80
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.76
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.77
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.38
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.03
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.77
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.45
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.65
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.74e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.74e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.71
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.65
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.64
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:34.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11716.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000011218

Normal statistic for number of bits   :   0.089
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.59
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999865097

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.21
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.32
p-value of test                       :    0.99

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:32.37

 All tests were passed




Server wird beendet - Lösche Semaphor 44728342.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5433
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:13.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.85
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.24
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  531.22
p-value of test                       :  9.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.05
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.08
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.69
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4836.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908028
  j =  2                              :            45977
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46221
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870221
  j =  1                              :        399907561
  j =  2                              :            46215
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  5.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.27e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.00
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.37
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.40
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.82
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.60
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.17
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.74
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.41
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.37
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.70
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.83
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.05e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9882.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5057.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.51
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.46
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.00
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.02
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.06
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999980327

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.92
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000033142

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.085
p-value of test                       :    0.47

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.0e-3

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.44
p-value of test                       :  7.4e-3

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:36.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     9.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45613078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9923

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.14
p-value of test                       :    0.9991    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:41.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.16
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.33
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.68
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7113.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5290.14
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46178
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870178
  j =  1                              :        399907649
  j =  2                              :            46168
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908065
  j =  2                              :            45957
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.6e-3

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    3.00
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.29
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17399.27
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.62
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.80
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.33
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.93
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.90
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.96
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.84
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.80
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.53
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.89
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.72
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.58
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.39
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.80
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.66
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.03
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4738.84
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000041527

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.40
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000131584

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.089
p-value of test                       :    0.46

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:42.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46530582.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1505
p-value of test                       :  9.2e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334625
  j =  1                              :        599996990
  j =  2                              :             1505
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7498
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6951.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.28
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.90
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.39
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908436
  j =  2                              :            45776
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45323
p-value of test                       :    0.9953


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869323
  j =  1                              :        399909357
  j =  2                              :            45317
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.96
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.19
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.09
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.32
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.33
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.32
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.24
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.92
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.26
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.52
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.49
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.14
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.75
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.74
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.71
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9647.23
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9909.75
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.33
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4790.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.22
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.47
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.97
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000124036

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.91
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999903059

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:53.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           9.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47480854.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4169
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     976
p-value of test                       :  6.4e-3

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     564
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.37
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.03
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:56.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45772
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869772
  j =  1                              :        399908456
  j =  2                              :            45772
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45703
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869703
  j =  1                              :        399908598
  j =  2                              :            45695
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-5
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.027
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.46
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.31
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17459.01
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.50
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.63
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.18
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.66
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.64
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.97
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.11
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.65e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.43e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.02
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.052
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:20.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12035.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.35
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.62
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999966830

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.55
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999991196

Normal statistic for number of bits   :  -0.070
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.29

 All tests were passed




Server wird beendet - Lösche Semaphor 48529430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4506
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7262.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.41
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.22
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45495
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869495
  j =  1                              :        399909011
  j =  2                              :            45493
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908438
  j =  2                              :            45772
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.56e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.75
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17639.55
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.11
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.68
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.07
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.79
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.14
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.15
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.46
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.64
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4892.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.55
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.97
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.16
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.22
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.26
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10158.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.52
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.22
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000079666

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.68
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999955217

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.39
p-value of test                       :  8.4e-3

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:12.26

 All tests were passed




Server wird beendet - Lösche Semaphor 49512470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    2.63
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.54
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.07
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.64
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.23
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.17
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46038
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870038
  j =  1                              :        399907927
  j =  2                              :            46032
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908374
  j =  2                              :            45804
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 6.14e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.18
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.36
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.79
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.44
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.55
p-value of test                       :  6.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   63.08
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.25
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.21
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.91
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.65
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.26
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.16
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.97
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.18
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.19
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.67
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.96
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.25e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.30
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10029.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:04:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.72
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4249.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.14
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.16
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999960599

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.45
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999978551

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.37

 All tests were passed




Server wird beendet - Lösche Semaphor 50462742.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.83
p-value of test                       :  3.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.22
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.73
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.38
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7124.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.21
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5071.86
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907919
  j =  2                              :            46036
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907822
  j =  2                              :            46080
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.73e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.41
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.72
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.46
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.30
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  428.47
p-value of test                       :    0.9908


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.75
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.91
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.09
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.62
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.33
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5107.94
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.72
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.39
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.41
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.53
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.08e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 7.88e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.69
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5105.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.25
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.64
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11679.29
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.41
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000010804

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.83
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000032860

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.07

 All tests were passed




Server wird beendet - Lösche Semaphor 51511318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:09.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.13
p-value of test                       :    0.9996    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6907.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.61
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.24
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5162.60
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:54.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908291
  j =  2                              :            45853
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45523
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869523
  j =  1                              :        399908961
  j =  2                              :            45509
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.23e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.74
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.57
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.06
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17229.26
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.25
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.56
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.94
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.56
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.34
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.66
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.33
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.61
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.21
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.20
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.36
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.55
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.68
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.46
p-value of test                       :    0.9913


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.53e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.47
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.61
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:39.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4662.00
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.29
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.70
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.83
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000016987

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.58
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000104509

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.71
p-value of test                       :  3.4e-3

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:10.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52592662.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     961
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.28
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.87
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.05
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.60
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.49
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:00.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908256
  j =  2                              :            45860
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46083
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870083
  j =  1                              :        399907839
  j =  2                              :            46073
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:32.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.91e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 3.15e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.87
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.12
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.62
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.92
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.25
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.30
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.97
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.78
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:42.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.58
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.07
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.78
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.52
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.08
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.46e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.33
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.75
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.56
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000145867

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.11
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999978770

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.22
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    2.74
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:49.56

 All tests were passed




Server wird beendet - Lösche Semaphor 53739542.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    6.78
p-value of test                       :  4.3e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     816
p-value of test                       :    0.9976

Stat. AD (mNP2)                       :    0.13
p-value of test                       :    0.9995    *****

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:41.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.65
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.61
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.97
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7079.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.33
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.85
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.15
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.52
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:59.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45789
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869789
  j =  1                              :        399908425
  j =  2                              :            45783
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908312
  j =  2                              :            45838
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.21e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.50
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : -8.52e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.98
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.84
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.48
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17252.57
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.12
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.91
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.15
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.89
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.37
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.75
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.01
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.51
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.36
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.79
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.81
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.11
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.11
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.13
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.09
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.53
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.1e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    6.56
p-value of test                       :  5.8e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9586.11
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.015
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4686.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.11
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.52
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.17
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999941648

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.76
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000045829

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.44e-4
p-value of test                       :    0.9990    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.68
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP1, t = 3          4.3e-4
 22  ClosePairs mNP2, t = 3          0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54788118.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1262
p-value of test                       :    0.9973

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334382
  j =  1                              :        599997476
  j =  2                              :             1262
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5512
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    3.51
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.56
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.10
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.05
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6858.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.28
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.06
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.61
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908341
  j =  2                              :            45822
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.33
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.11
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.44
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.48
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.72
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.55
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.51
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.31
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.25
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.94
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.39
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.26
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.35
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.57
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.92
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.95
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.61
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 6.62e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.20
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.05
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11767.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.63
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.69
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999956441

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.98
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000008383

Normal statistic for number of bits   :   0.066
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.48

 All tests were passed




Server wird beendet - Lösche Semaphor 55836694.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:05.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   41.35
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1510.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.78
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.47
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4916.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907901
  j =  2                              :            46042
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907949
  j =  2                              :            46024
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:30.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.20
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.89
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17682.51
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.98
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.15
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.88
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.58
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.46
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.03
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.33
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5275.24
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.82
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.93
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.00
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  238.39
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.39
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.31
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.84
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.86
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.69e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.72
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10043.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:20.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11787.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11732.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.02
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000017113

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.96
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000068038

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    2.52
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.68

 All tests were passed




Server wird beendet - Lösche Semaphor 56852502.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5279
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.92
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     984
p-value of test                       :  3.0e-3

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  189.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:21.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.13
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45664
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869664
  j =  1                              :        399908676
  j =  2                              :            45656
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45489
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869489
  j =  1                              :        399909027
  j =  2                              :            45479
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:32.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.50
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.86
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.54
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  167.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.89
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.90
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.79
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.45
p-value of test                       :    0.9929


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.53
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.97
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.69
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.98
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.37
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.22
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.35
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.13
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.50e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.97e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.93
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9690.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11515.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.62
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999926807

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.51
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000018376

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:42.30

 All tests were passed




Server wird beendet - Lösche Semaphor 57901078.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7093
p-value of test                       :    0.9959


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    3.54
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.38
p-value of test                       :  2.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    5.14
p-value of test                       :  2.5e-3

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:41.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.45
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.85
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.10
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.06
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6952.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.62
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.31
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908338
  j =  2                              :            45825
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907697
  j =  2                              :            46147
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  1.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    4.40
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9948


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.64
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.80
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.89
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.61e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17095.48
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.46
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.96
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.88
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.92
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.33
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.22
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  102.19
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.12
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.91
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.59
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.06
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.09
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.76e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.52
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.63
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:19.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.50
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.52
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000178807

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999833702

Normal statistic for number of bits   :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.15
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.07

 All tests were passed




Server wird beendet - Lösche Semaphor 59015190.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997261
  j =  2                              :             1368
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.07
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.27
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.50
p-value of test                       :  5.5e-3


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.56
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45752
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869752
  j =  1                              :        399908496
  j =  2                              :            45752
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45205
p-value of test                       :    0.9992    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869205
  j =  1                              :        399909592
  j =  2                              :            45201
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:29.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.61
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.35
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17126.07
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.95
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.11
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.86
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.09
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.53
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.12
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.52
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.17
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.49
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.21
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.87
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.91
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.79
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.96
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.21
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.69e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.29
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.71
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.25
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.64
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.70
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999947369

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.76
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000041950

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.099
p-value of test                       :    0.54

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:11.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 45  CollisionPermut, r = 10         0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60030998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.40
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.99
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.43
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.51
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7230.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.26
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.97
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.48
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.28
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:58.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46206
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870206
  j =  1                              :        399907590
  j =  2                              :            46202
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908522
  j =  2                              :            45736
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.80
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.78
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.38
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.53
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.58
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.39
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.17
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.88
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.69
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.02
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.57
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.20
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.73
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.22
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.68
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.63
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   37.51
p-value of test                       :  1.8e-4    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -2.14
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.85
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.93e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.80
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.88
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.55
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9911.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4700.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.84
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3965.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11555.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.73
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999932792

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.93
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000068728

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               1.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61079574.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.77
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    3.25
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     262
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:46.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.24
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.78
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.44
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6950.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:58.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.65
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:47.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.82
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:41.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4853.63
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45267
p-value of test                       :    0.9979


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869267
  j =  1                              :        399909473
  j =  2                              :            45253
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45454
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869454
  j =  1                              :        399909095
  j =  2                              :            45448
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 3.92e-4
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.99
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.67
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17685.89
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.76
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.99
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.35
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.40
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.04
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.53
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.54
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.40
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.67
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.05
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.95
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4771.67
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.70
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.55
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.76
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.16
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.87e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.85
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.94
p-value of test                       :    0.9986

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.01
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.23
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999846380

Normal statistic for number of bits   :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.68
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999937739

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:02.11

 All tests were passed




Server wird beendet - Lösche Semaphor 62128150.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1508.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7063.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.61
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.05
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.09
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908822
  j =  2                              :            45577
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908419
  j =  2                              :            45786
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.18e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:34.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.67e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.99
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.05
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.36
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.95
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.71
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.23
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.63
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.08
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.93
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.61
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:47.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.79
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.41
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.47
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.78
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.77
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.32
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.97
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.84
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.9901

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 8.03e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.60
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.32
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9933.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.13
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999898961

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.36
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999910316

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:19:56.78

 All tests were passed




Server wird beendet - Lösche Semaphor 42696727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4470
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.03
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.39
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.62
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.62
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.30
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.49
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.29
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:21.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46332
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870332
  j =  1                              :        399907338
  j =  2                              :            46328
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908654
  j =  2                              :            45670
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:34.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.70
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.93
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.03
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.86
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17358.58
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.02
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.35
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.77
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.24
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.74
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.91
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.59
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4937.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.34
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.43
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.04
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.48
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:33.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.99
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:19.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.05
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -1.79
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.62
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.42
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.94
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.043
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.70
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:04:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.50
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999997664

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.05
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000110623

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:04.01

 All tests were passed




Server wird beendet - Lösche Semaphor 43221010.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7045
p-value of test                       :    0.9993    *****


-----------------------------------------------
CPU time used                    :  00:03:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9961

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.30
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.22
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.14
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.13
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5052.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907795
  j =  2                              :            46095
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:33.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.077
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.86
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.76
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  157.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.27
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.00
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.35
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.23
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.64
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.09
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.78
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.61
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.12
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  140.40
p-value of test                       :    0.9995    *****


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.82
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.08
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.49
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.01
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.64
p-value of test                       :  8.7e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.84e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.91e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.16
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.06
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.95
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.58
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.26
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.96
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999964820

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.68
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000083041

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    2.47
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :  -0.097
p-value of test                       :    0.54

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:34.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        0.9993 
 78  RandomWalk1 C (L=10000, r=0)    0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44564498.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.66
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  358.56
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6942.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.83
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.32
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908689
  j =  2                              :            45648
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45814
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869814
  j =  1                              :        399908376
  j =  2                              :            45806
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:33.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.16e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17698.80
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.83
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.41
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.27
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.41
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.65
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.89
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.89
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.18
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.73
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.42
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.77
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.48
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.78
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.66
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.49
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.74
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.07
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.42
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.65
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.15
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.12
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.60
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.51
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000000985

Normal statistic for number of bits   : 7.79e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.48
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999820082

Normal statistic for number of bits   :   -1.42
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:13.12

 All tests were passed




Server wird beendet - Lösche Semaphor 45449234.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7083
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.55
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1453.69
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.39
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.58
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46154
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870154
  j =  1                              :        399907698
  j =  2                              :            46142
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907763
  j =  2                              :            46105
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.17e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.54e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17618.62
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.09
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.92
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.22
p-value of test                       :  4.3e-3


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.31
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.06
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.12
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.92
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.10
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.79
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.20
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.58
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.18
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.48
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.78e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.85e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.36
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.93
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.56
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999997115

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.65
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999760685

Normal statistic for number of bits   :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:40.96

 All tests were passed




Server wird beendet - Lösche Semaphor 46333970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5306
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4494
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     822
p-value of test                       :    0.9956

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9988

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.86
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.56
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1334.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.82
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:09.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.40
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.89
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:01.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45449
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869449
  j =  1                              :        399909105
  j =  2                              :            45443
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869535
  j =  1                              :        399908933
  j =  2                              :            45529
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.10e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17230.49
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.61
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.68
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.78
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.42
p-value of test                       :  1.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.42
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.95
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.90
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.46
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.80
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.51
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5142.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.88
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.99
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.58
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.29
p-value of test                       :    0.99

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.95e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.90
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.03
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.56
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.68
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.03
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.08
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.17
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.36
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.22
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000140956

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.49
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000214702

Normal statistic for number of bits   :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:38.13

 All tests were passed




Server wird beendet - Lösche Semaphor 47317010.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    4.44
p-value of test                       :  5.3e-3

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.24
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.40
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.04
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7175.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.86
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.71
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.58
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4905.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:55.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907992
  j =  2                              :            46001
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45979
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869979
  j =  1                              :        399908046
  j =  2                              :            45971
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.78e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.33
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.62
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.38
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.78
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.67
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.21
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.99
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.08
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.00
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.06
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.12
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.14
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.79
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.12
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.62
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.71
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.80
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.05
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.50
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.61
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.83e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.33
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.37
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.06
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000061048

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.61
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000011683

Normal statistic for number of bits   :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.22e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9944

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:52.78

 All tests were passed




Server wird beendet - Lösche Semaphor 48365586.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5517
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.35
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.53
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.88
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.22
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.44
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.32
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.99
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908176
  j =  2                              :            45903
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908737
  j =  2                              :            45627
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.58e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.20
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.35
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.44
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.25
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.80
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.17
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.94
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.94
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.89
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  116.44
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.79
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.89
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.65
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.19
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.40
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.86
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.39
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.41
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.02
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.77
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.03
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.22e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   42.00
p-value of test                       :  1.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.07
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:33.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.95
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.46
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4183.43
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.88
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.31
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000054046

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.56
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999916856

Normal statistic for number of bits   :   -0.66
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.1e-4    *****

Anderson-Darling statistic = A2       :    5.73
p-value of test                       :  1.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.74
p-value of test                       :  3.1e-3

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.30

 All tests were passed




Server wird beendet - Lösche Semaphor 49381394.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1265
p-value of test                       :    0.9966

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334385
  j =  1                              :        599997470
  j =  2                              :             1265
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7548
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  279.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.45
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6895.17
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   15.55
p-value of test                       :  8.3e-3


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.93
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.18
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:58.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908315
  j =  2                              :            45841
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45627
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869627
  j =  1                              :        399908748
  j =  2                              :            45623
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 3.73e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.074
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.58
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.11
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17200.70
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.39
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.82
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5136.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5241.87
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.89
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.59
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.29
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.90
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.00
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000042961

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.23
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000076399

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:07.88

 All tests were passed




Server wird beendet - Lösche Semaphor 50429970.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1250
p-value of test                       :    0.9991    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334370
  j =  1                              :        599997500
  j =  2                              :             1250
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.47
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.45
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.99
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.46
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.25
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5369.69
p-value of test                       :  6.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908795
  j =  2                              :            45595
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907518
  j =  2                              :            46235
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:29.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.69
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.01
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17434.43
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.32
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.22
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.83
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.16
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.95
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.58
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.86
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.56
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  309.98
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.99
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.55
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.34
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.63
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10160.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10123.78
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.95
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.65
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999986624

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.70
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000005890

Normal statistic for number of bits   :   0.047
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:48.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9991 
 42  Permutation, t = 7              6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51478546.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.44
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.17
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.49
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.68
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5137.14
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:54.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907872
  j =  2                              :            46058
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907794
  j =  2                              :            46091
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.51e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.89
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.64
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17446.47
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.82
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.17
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.41
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.69
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.64
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.46
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.71
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.23
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5190.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.28
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.67
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.00
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.70
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.72
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.69e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10324.23
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.55
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.98
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:33.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12109.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.62
p-value of test                       :  7.3e-3


-----------------------------------------------
Total number of bits:  8000076057

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.80
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000123934

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:15.60

 All tests were passed




Server wird beendet - Lösche Semaphor 52527122.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.18
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.22
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.41
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.30
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.52
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.05
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.20
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.74
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45390
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869390
  j =  1                              :        399909220
  j =  2                              :            45390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907783
  j =  2                              :            46107
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.15
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.92
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.34
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.05
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17113.56
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.21
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   48.48
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.72
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.86
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.93
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.65
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4924.94
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.79
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5118.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.40
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.94
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 9.38e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.77
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.49
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:33.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.90
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999940187

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.05
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999885410

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.3e-3

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    7.49
p-value of test                       :  2.2e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -3.71
p-value of test                       :    0.9999    *****

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:26.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 104  AutoCor, d=3, r=0               0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53575698.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997367
  j =  2                              :             1315
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4458
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.98
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.58
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.35
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7187.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.55
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.92
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.73
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908138
  j =  2                              :            45919
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908064
  j =  2                              :            45962
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904


-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    4.34
p-value of test                       :  6.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9985


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.04e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.00
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.63
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.71
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.17
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   59.60
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.83
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.13
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.63
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.91
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.11
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.24
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.16
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.68
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.38
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9955

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.28e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    : 6.73e-3
p-value of test                       :    0.9929

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  146.79
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:04:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.90e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4714.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.54
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.48
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.89
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999967688

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.52
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999986336

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.31

 All tests were passed




Server wird beendet - Lösche Semaphor 54624274.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5531
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4145
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:05.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.82
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.19
p-value of test                       :  2.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.40
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.61
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908468
  j =  2                              :            45766
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907892
  j =  2                              :            46051
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.61e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.98
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.21
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17272.02
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.60
p-value of test                       :    0.9947


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.20
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.86
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.90
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.73
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.52
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.94
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.62
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.06
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.32
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.00
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.79
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.62e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.76e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.06
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.089
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12058.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.87
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999938927

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.61
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000137836

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:23.19

 All tests were passed




Server wird beendet - Lösche Semaphor 55640082.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:02.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7139
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9939


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     948
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.35
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    4.06
p-value of test                       :  8.1e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    4.74
p-value of test                       :  3.8e-3

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.14
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.50
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.09
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.23
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46114
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870114
  j =  1                              :        399907775
  j =  2                              :            46108
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907881
  j =  2                              :            46055
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.4e-3


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:20.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.40e-3
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.17
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.52
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.09
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.37
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17249.39
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.05
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.21
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.04
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.63
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.31
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.67
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.30
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  271.68
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.89
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.08
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.04
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.89
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.35
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.25
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.78
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    1.66
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    2.70
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.15
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.12
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.74
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000140776

Normal statistic for number of bits   :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.48
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000019006

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:38.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 C (L=10000, r=0)    5.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56721426.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.05
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.56
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.17
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.46
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:05.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908363
  j =  2                              :            45811
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908616
  j =  2                              :            45689
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.36e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 5.05e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.37
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.74
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.49
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.03
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.34
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.81
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.00
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.23
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.03
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.95
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.95
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.71
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.20
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4981.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.09
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.14e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 6.86e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.82
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.63
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10022.38
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.13
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4967.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.09
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11696.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.47
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999892622

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.23
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000029845

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:09.78

 All tests were passed




Server wird beendet - Lösche Semaphor 57835538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.09
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6920.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.41
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.79
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.00
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:01.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908517
  j =  2                              :            45737
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908317
  j =  2                              :            45840
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.84e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.73e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.77
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.40
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.91
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.90
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.13
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.00
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.55
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.78
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.74
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.25
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.04
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.27
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.22
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.02
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4893.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.61
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-3
p-value of test                       :    0.9914

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -2.95e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   30.24
p-value of test                       :    0.9963


-----------------------------------------------
Total number of bits:  8000051313

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.45
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999927254

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.71

 All tests were passed




Server wird beendet - Lösche Semaphor 58851346.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9921

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9918

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.43
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.04
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.66
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.60
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:35.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4994.88
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:59.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908480
  j =  2                              :            45760
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46158
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870158
  j =  1                              :        399907688
  j =  2                              :            46150
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:29.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.89
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17683.63
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.48
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.90
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.35
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.91
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.85
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  422.43
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.81
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.70
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.50
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.39
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.35
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.70
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.076
p-value of test                       :    0.53

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.47
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9899.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.22
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:15.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  2.2e-4    *****

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4006.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.90
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12000.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.84
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000141730

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.13
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999973907

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 5.12e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.68
p-value of test                       :    0.9963

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :  -0.013
p-value of test                       :    0.51

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:38.70

 All tests were passed




Server wird beendet - Lösche Semaphor 59867154.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.27
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:07.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.40
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4972.27
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:10.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908674
  j =  2                              :            45657
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46207
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870207
  j =  1                              :        399907593
  j =  2                              :            46193
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.98
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.69
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.61
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.81
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.14
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.24
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.54
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.83
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.30
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.89
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.29
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.63
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.36
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.40
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.96
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.45
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.44
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.66
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.81
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.95
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10175.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4764.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4336.12
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11602.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.17
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999980147

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.75
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000109249

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.89

 All tests were passed




Server wird beendet - Lösche Semaphor 60882962.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.33
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.03
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  278.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.60
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5025.93
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46084
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870084
  j =  1                              :        399907834
  j =  2                              :            46080
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46163
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870163
  j =  1                              :        399907679
  j =  2                              :            46153
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.99e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.22
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.45
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.58
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.55
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.87
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.53
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.00
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.06
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.64
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.25
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.54
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.12
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5185.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.03
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.02
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.62
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.22
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.71e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.77
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.39
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.23
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.60
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4772.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.76
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11591.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11702.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000090388

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.51
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000039160

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:37.44

 All tests were passed




Server wird beendet - Lösche Semaphor 61931538.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:19.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:05:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    2.78
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.89
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.03
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.05
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.46
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.37
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.94
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.40
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.69
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908114
  j =  2                              :            45937
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45446
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869446
  j =  1                              :        399909114
  j =  2                              :            45434
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:35.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.87e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.74e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.19e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.93
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.23
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17085.94
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.42
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.34
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.24
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.66
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.72
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.96
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.32
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.73
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.02
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.94
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.09
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.76
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.43
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.08
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:14.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.80e-3
p-value of test                       :    0.9905

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.99
p-value of test                       :    0.98

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.50e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.46e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.60
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.33
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.14
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4180.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11573.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.54
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000045958

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.76
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000156097

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:30:05.88

 All tests were passed




Server wird beendet - Lösche Semaphor 42729496.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7129
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.04
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7163.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.71
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.11
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.35
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46283
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870283
  j =  1                              :        399907442
  j =  2                              :            46267
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46401
p-value of test                       :  7.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870401
  j =  1                              :        399907201
  j =  2                              :            46395
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:47.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.49
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17617.48
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   61.19
p-value of test                       :  4.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.04
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.27
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.38
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  114.40
p-value of test                       :  1.8e-3


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  453.87
p-value of test                       :  8.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.58
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5222.53
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.44
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.98
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.95
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.85
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.93
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10286.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5034.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.95
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.63
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11917.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.07
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999948593

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.57
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000019996

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:26.21

 All tests were passed




Server wird beendet - Lösche Semaphor 43581464.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:54.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    3.64
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.60
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.24
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.55
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.77
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5238.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45380
p-value of test                       :    0.9902


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869380
  j =  1                              :        399909243
  j =  2                              :            45374
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46216
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870216
  j =  1                              :        399907571
  j =  2                              :            46210
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.53
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17455.61
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.00
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.71
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.86
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.63
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.14
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.94
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.80
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.46
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.12
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.16
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.68
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.66
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.59
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.47e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.40e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.22
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.94
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.51
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12337.25
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11983.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:34.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.99
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000176065

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.37
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000088159

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:06.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 99  HammingIndep, L=1200, r=0       5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44269592.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1259
p-value of test                       :    0.9979

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334379
  j =  1                              :        599997482
  j =  2                              :             1259
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5283
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.48
p-value of test                       :  5.2e-3

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.80
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.09
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.39
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.12
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6866.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.48
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.51
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.64
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5061.40
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46612
p-value of test                       :  3.3e-4    *****


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870612
  j =  1                              :        399906780
  j =  2                              :            46604
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907819
  j =  2                              :            46086
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 4.64e-4
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.72
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.86
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.79
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17547.08
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.66
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.22
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.29
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.19
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.77
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.40
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.65
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.70
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.70
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  255.37
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.16e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   45.00
p-value of test                       :  1.4e-4    *****



-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.20
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:28.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.18
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4931.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.58
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999902333

Normal statistic for number of bits   :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.85
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000009913

Normal statistic for number of bits   :   0.078
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:42.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 44  CollisionPermut, r = 0          3.3e-4
 86  LongestHeadRun, r = 0           1.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45383704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:02:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.95
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.77
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.74
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.99
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908141
  j =  2                              :            45922
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907931
  j =  2                              :            46027
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:05:01.31

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


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CPU time used                    :  00:02:31.84

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  8.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.54
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9982


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


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CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


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CPU time used                    :  00:01:53.32

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.57
p-value of test                       :    0.01


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CPU time used                    :  00:02:10.47

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

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CPU time used                    :  00:01:56.89

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

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CPU time used                    :  00:01:20.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

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CPU time used                    :  00:01:38.68

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.16e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

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CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 3.40e-4
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

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CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

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CPU time used                    :  00:00:25.06

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

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CPU time used                    :  00:00:25.09

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

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CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

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CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   88.84
p-value of test                       :    0.04

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CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

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CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   70.52
p-value of test                       :    0.36

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CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.70
p-value of test                       :    0.72

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CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   35.79
p-value of test                       :    0.53

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CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

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CPU time used                    :  00:00:58.52

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   29.47
p-value of test                       :    0.44

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CPU time used                    :  00:01:50.12

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.98
p-value of test                       :    0.70

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CPU time used                    :  00:01:05.15

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.83
p-value of test                       :    0.94

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CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


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Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.44

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CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

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CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

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CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

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CPU time used                    :  00:01:07.81

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.77
p-value of test                       :    0.12

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CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17841.64
p-value of test                       :    0.01



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CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.44
p-value of test                       :    0.28


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Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.44
p-value of test                       :    0.87


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.94
p-value of test                       :    0.36


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


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CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.65
p-value of test                       :    0.53


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.08
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.32
p-value of test                       :    0.17


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.06
p-value of test                       :    0.02


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CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.38
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.36
p-value of test                       :    0.45


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.46
p-value of test                       :    0.26


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CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.44
p-value of test                       :    0.26


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.26
p-value of test                       :    0.95


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CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.61
p-value of test                       :    0.73


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.44
p-value of test                       :    0.61


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.40
p-value of test                       :    0.92


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.71
p-value of test                       :    0.19


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CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.52
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.61
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4812.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.76
p-value of test                       :    0.14


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.50
p-value of test                       :    0.24


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CPU time used                    :  00:00:37.11

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.26
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



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CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



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CPU time used                    :  00:02:26.43

Generator state:




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HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.41
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10319.56
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:34.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.00
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.79
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4228.95
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.30
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.40
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000044209

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.44
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999943211

Normal statistic for number of bits   :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:27.50

 All tests were passed




Server wird beendet - Lösche Semaphor 46497816.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.23
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.40
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.33
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.13
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.92
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:59.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907681
  j =  2                              :            46155
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908501
  j =  2                              :            45745
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.98e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.32
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.96
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.13
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.16
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17773.47
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.83
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.23
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.66
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.46
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  409.15
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.16
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.09
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.74
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.93
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  456.94
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.40
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.51
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.86
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:09.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.67
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4275.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.66
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000052672

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.79
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000042913

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    3.04
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:45.46

 All tests were passed




Server wird beendet - Lösche Semaphor 47841304.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:40.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.95
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.96
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.40
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   90.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.06
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45652
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869652
  j =  1                              :        399908700
  j =  2                              :            45644
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908570
  j =  2                              :            45712
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.83e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.028
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.82
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.85
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.70
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.93
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.58
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.58
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.13
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.46
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.83
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.09
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.96
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.57
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.77
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.84
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.86
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.14
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.55
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.91
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.98
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:32.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.19
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000020182

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   99.62
p-value of test                       :  1.6e-4    *****


-----------------------------------------------
Total number of bits:  7999946901

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:45.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             1.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48758808.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4459
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.61
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.91
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.76
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.81
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.90
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:59.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907856
  j =  2                              :            46069
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908464
  j =  2                              :            45762
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.59
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.20
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    5.82
p-value of test                       :  1.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   78.01
p-value of test                       :  3.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17367.95
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.45
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.64
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.40
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.66
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.90
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.52
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.18
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.76
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.21
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.16
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.34
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.98
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.81
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.01
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.39
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.40
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.31
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.95
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.98
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.55e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.46
p-value of test                       :    0.9933

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.27
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12034.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.11
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000096262

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.77
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999978692

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:40.80
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 66  MatrixRank, L=30, r=0           3.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49741848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4499
p-value of test                       :  7.3e-3


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7167
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.44
p-value of test                       :  5.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.99
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.47
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.67
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7289.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:11.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.14
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.30
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:02.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908017
  j =  2                              :            45984
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907567
  j =  2                              :            46212
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.9930

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:33.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.73e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.9966

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.98e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 8.58e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.72e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.66
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.03
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.00
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17625.87
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.08
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.87
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.25
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.26
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.84
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.46
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.80
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.24
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.29
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.41
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.10
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.82
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4879.11
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.97
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.86
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.53
p-value of test                       :    0.9980


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.89
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.55
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10231.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.19
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.69
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000015001

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.01
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000075994

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:04.90

 All tests were passed




Server wird beendet - Lösche Semaphor 50626584.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5233
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:03:54.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    5.10
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.30
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.31
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6794.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.89
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5145.24
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46109
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870109
  j =  1                              :        399907785
  j =  2                              :            46103
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45823
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869823
  j =  1                              :        399908358
  j =  2                              :            45815
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    : 4.35e-3
p-value of test                       :    0.9951

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.10e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.35
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.20
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:41.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17143.15
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.38
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.77
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.08
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.54
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.97
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.99
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.45
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.87
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.72
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.15
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.50
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.91
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.99
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.41
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.74e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.72
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.64
p-value of test                       :    0.9902

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.24
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4314.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.05
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11951.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:34.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.96
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999757388

Normal statistic for number of bits   :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.46
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000028447

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :  -0.063
p-value of test                       :    0.53

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:09.96

 All tests were passed




Server wird beendet - Lösche Semaphor 52035608.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.29
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.92
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7147.24
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.29
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.10
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4895.78
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:57.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46195
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870195
  j =  1                              :        399907616
  j =  2                              :            46183
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46054
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870054
  j =  1                              :        399907894
  j =  2                              :            46050
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:02:32.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 3.54e-4
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.41
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.90
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.81
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.17
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.73
p-value of test                       :    0.9933


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.66
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.62
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.53
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.53
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.28
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.91
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.79
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.48
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.62
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.24e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.81e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.00
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.05
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10169.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.57
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000000301

Normal statistic for number of bits   : 2.38e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.61
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999965771

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    3.09
p-value of test                       :  1.0e-3

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:04.35

 All tests were passed




Server wird beendet - Lösche Semaphor 52985880.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5323
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.15
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.69
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.65
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  486.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7023.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.42
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5042.66
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45664
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869664
  j =  1                              :        399908677
  j =  2                              :            45654
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908193
  j =  2                              :            45893
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.86e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.53
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.54
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.84
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.93
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.47
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.74
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.31
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.43
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.33
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.98
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.42
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4802.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.90
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.26
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.52
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.70
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.56e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.69
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.46
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.050
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.31
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4330.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11562.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11429.32
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.62
p-value of test                       :    0.9906


-----------------------------------------------
Total number of bits:  8000075754

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.89
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999972413

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.23e-3
p-value of test                       :    0.9956

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.42
p-value of test                       :    0.9923

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:47.51

 All tests were passed




Server wird beendet - Lösche Semaphor 54099992.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5409
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:11.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.32
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.72
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1427.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7326.43
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:10.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.95
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.58
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.09
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908105
  j =  2                              :            45946
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907909
  j =  2                              :            46044
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:31.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.85e-3
p-value of test                       :    0.9902

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.48
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.27
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.32
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.04
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.18
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.43
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.61
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.09
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.62
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.19
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.52
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.69
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.04
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.32
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.61
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.31
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.44
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.10e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.94
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.90
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11546.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.39
p-value of test                       :  1.4e-3


-----------------------------------------------
Total number of bits:  8000082843

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:09.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.34
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000160645

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.5e-3

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.35
p-value of test                       :  9.4e-3

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:05.69

 All tests were passed




Server wird beendet - Lösche Semaphor 55148568.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7504
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :  105.91
p-value of test                       :  3.1e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.28
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5021.20
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:00.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46318
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870318
  j =  1                              :        399907366
  j =  2                              :            46314
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908610
  j =  2                              :            45692
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.75e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.24e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.20
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.68
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.27
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.43
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.52
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.84
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.84
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.37
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.17
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.50
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.28
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.82
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.73
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4960.20
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.73
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.98
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.89
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    1.35
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.42e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.95e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5024.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:33.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.82
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.96
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999850019

Normal statistic for number of bits   :   -1.19
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.16
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000004951

Normal statistic for number of bits   :   0.039
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    5.90
p-value of test                       :  1.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.31
p-value of test                       :  4.7e-4    *****

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:46.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         3.1e-5
 54  SampleMean, r = 10              0.9992 
 103  AutoCor, d=1, r=0               4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56393752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7161
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7199
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:52.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:46.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.25
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.39
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.82
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.33
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:39.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1555.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.54
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.99
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.80
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5164.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45830
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869830
  j =  1                              :        399908343
  j =  2                              :            45824
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908050
  j =  2                              :            45969
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:34.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.77
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.12
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.24
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.90
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.35
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.85
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.97
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.34
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.21
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.64
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.17
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.28
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.12
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.27
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.87
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.51
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -2.54
p-value of test                       :    0.9944



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.40
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.22
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.88e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.67
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.36
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  244.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.50
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.79
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.18
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.84
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.78
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000142810

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.93
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999842837

Normal statistic for number of bits   :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:55.37

 All tests were passed




Server wird beendet - Lösche Semaphor 57507864.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5370
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    4.12
p-value of test                       :  7.6e-3

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.67
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1433.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7020.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.13
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:06.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45502
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869502
  j =  1                              :        399908998
  j =  2                              :            45498
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908645
  j =  2                              :            45673
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.07e-4
p-value of test                       :    0.9996    *****

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 1.18e-5
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.92e-6
p-value of test                       :    0.9961

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.28
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.12
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.36
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17783.92
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.05
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.48
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.46
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.40
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.32
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.66
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.14
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.90
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.90
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4742.69
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.07
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4993.89
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.94
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.30
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.74
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.41
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.21
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9728.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:04:10.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11619.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.67
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000125905

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.56
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999967781

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:42.64

 All tests were passed




Server wird beendet - Lösche Semaphor 58589208.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.1e-3

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.30
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.18
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7046.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.70
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5029.25
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:05.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908206
  j =  2                              :            45894
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908140
  j =  2                              :            45927
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.35e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9920


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.42
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.03
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :  1.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    5.44
p-value of test                       :  1.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   19.48
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17401.79
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.43
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.68
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.56
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.23
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.64
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.71
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.55
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.39
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.59
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.26
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.68
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.59
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.88
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.00
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.97
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.55
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11751.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.71
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999864230

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.23
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999941345

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:08.84

 All tests were passed




Server wird beendet - Lösche Semaphor 59572248.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9985


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.09
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.58
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6948.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.64e-3
p-value of test                       :    0.9952

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.79
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.12
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5099.61
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45828
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869828
  j =  1                              :        399908346
  j =  2                              :            45824
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45855
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869855
  j =  1                              :        399908292
  j =  2                              :            45851
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.70e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.66e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17221.02
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.65
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.28
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.78
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.97
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.67
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.82
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.72
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.24
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.52
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.75
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.07
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.73
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.03e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10062.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4782.80
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4959.62
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3976.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:34.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.96
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999817670

Normal statistic for number of bits   :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.48
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999951638

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:18.78

 All tests were passed




Server wird beendet - Lösche Semaphor 60620824.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.79
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.25
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.94
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.27
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908320
  j =  2                              :            45837
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46004
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870004
  j =  1                              :        399907993
  j =  2                              :            46002
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.08
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   65.72
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.13
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17214.02
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.93
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.61
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.34
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.90
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.81
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.07
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.99
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.34
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.04
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.40
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.18
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.19
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.50
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.60
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.95e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.58
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.37
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.21
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.59
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.58
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.073
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.67
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.18
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.27
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999993743

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.90
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000060391

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 6.22e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:53.48

 All tests were passed




Server wird beendet - Lösche Semaphor 61767704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.32
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    3.56
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.03
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.42
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1484.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7091.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.16
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.03
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.45
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45723
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869723
  j =  1                              :        399908556
  j =  2                              :            45719
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908287
  j =  2                              :            45852
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.88e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.40
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17723.10
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.39
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.23
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.89
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.40
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.74
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.36
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.42
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.42
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4897.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.64
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.85
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:32.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.35
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   43.00
p-value of test                       :  5.7e-4    *****



-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.27
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10075.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4277.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.91
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11554.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.99
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000033619

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.04
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999961646

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:01:12.57
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 86  LongestHeadRun, r = 0           5.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62783512.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4475
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7465
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.95
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    3.30
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.11
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.42
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.03
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.25
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.81
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.07
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.35
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:21.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908670
  j =  2                              :            45662
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907882
  j =  2                              :            46050
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.55
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.45
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.28
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.52
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.13
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.34
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.02
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.23
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.91
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.08
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.31
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.17
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.37
p-value of test                       :    0.9911

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.48e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.09e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.64
p-value of test                       :  5.6e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.98
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.97
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.66
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9718.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.56
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999925364

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.06
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999904334

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.9944

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:38.63

 All tests were passed




Server wird beendet - Lösche Semaphor 42762265.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5529
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7144
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.88
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     270
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.64
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.92
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.81
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.67
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6820.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.58
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.90
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.75
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5121.61
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45560
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869560
  j =  1                              :        399908880
  j =  2                              :            45560
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45546
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869546
  j =  1                              :        399908909
  j =  2                              :            45544
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.67e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.28e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 9.75e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.43
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.98
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17186.74
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.31
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.12
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.92
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.97
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   51.20
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.57
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.31
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.54
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.66
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.54
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.31
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.86
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.51
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.10
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.93
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.90
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:27.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.19e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.74
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.85
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.82
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10128.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.82
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.16
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.23
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.09
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999906680

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.04
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000042844

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.095
p-value of test                       :    0.46

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:17.28

 All tests were passed




Server wird beendet - Lösche Semaphor 43810841.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.79
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     828
p-value of test                       :    0.9920

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:03.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.79
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.54
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.59
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908455
  j =  2                              :            45762
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908209
  j =  2                              :            45891
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.94e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.33
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.43
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.68
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.83
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.99
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.64
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.50
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.93
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.17
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.73
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  577.80
p-value of test                       :  9.0e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.63
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.60
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.31
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.10
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.68
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.28
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.90
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  249.52
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.76
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.51
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    3.26
p-value of test                       :  5.5e-4    *****



-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.59
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9795.29
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:19.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.67
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.33
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999961784

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.84
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999976832

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:26.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 29              5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44892185.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5236
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:03:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4493
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:38.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.11
p-value of test                       : 1 -  4.8e-5    *****

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.12
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.69
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  271.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5076.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908145
  j =  2                              :            45917
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908039
  j =  2                              :            45976
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.61
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.46
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17151.35
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.27
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.98
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.33
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.02
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.27
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.38
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.72
p-value of test                       :    0.9925


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.59
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.71
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.37
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.83
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.31
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4851.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.82
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.61
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.95
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.53e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.62e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.95
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.50
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.75
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9995.70
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10125.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3978.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.17
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.45
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999958070

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.04
p-value of test                       :  5.5e-3


-----------------------------------------------
Total number of bits:  8000105880

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:40.32
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3         1 -  4.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45776921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:42.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4538
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.91
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.21
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.06
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.36
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.05
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.40
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908171
  j =  2                              :            45913
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.68e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.75
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.35
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.46
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.33
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.12
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.46
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.50
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.55
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.86
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.18
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.04
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.94
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.88
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.93
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.30
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10232.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10241.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:17.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.83
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.52
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:58.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.80
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3910.79
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.14
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:34.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.47
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000015535

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.33
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  7999763496

Normal statistic for number of bits   :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:18:26.03

 All tests were passed




Server wird beendet - Lösche Semaphor 46727193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9963

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.43
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.96
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.91
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.47
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6981.46
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:22.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.44
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:44.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5203.87
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:52.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907897
  j =  2                              :            46050
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.01
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.35
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17137.88
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.62
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :    9.20
p-value of test                       :    0.9983


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.57
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  202.11
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.88
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.46
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.90
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.65
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.41
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.12
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.23
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.75
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.42
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.11
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.72
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.13
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10226.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.05
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.69
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.05
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000027175

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.44
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000101431

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:43.22

 All tests were passed




Server wird beendet - Lösche Semaphor 48201753.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1263
p-value of test                       :    0.9971

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334383
  j =  1                              :        599997474
  j =  2                              :             1263
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:46.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7179
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:18.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.57
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.12
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1482.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.04
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:02.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45935
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869935
  j =  1                              :        399908133
  j =  2                              :            45929
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908655
  j =  2                              :            45668
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.86
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17055.85
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.02
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.86
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.22
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.84
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.53
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4836.93
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.23
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.48
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.78
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.66
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.78
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.62
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.92
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.75
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.30
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.14
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:29.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4724.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.96
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4052.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11586.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:33.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.71
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000095827

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.09
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999981686

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.97e-4
p-value of test                       :    0.9995    *****

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:40.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.41e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:25.94

 All tests were passed




Server wird beendet - Lösche Semaphor 49250329.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9937

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.47
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.47
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.79
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.65
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46094
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870094
  j =  1                              :        399907817
  j =  2                              :            46084
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908448
  j =  2                              :            45770
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:40.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    4.82
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:02:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.21
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.01
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17379.09
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.09
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.39
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.98
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.29
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.42
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.29
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.64
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.30
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.38
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.46
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.00
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.00
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.86
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4842.27
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.17
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.31
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.80e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.20
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.72
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11585.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.83
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.44
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999975704

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.14
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999832784

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:14.77

 All tests were passed




Server wird beendet - Lösche Semaphor 50331673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4160
p-value of test                       :    0.9965


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:59.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.80
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1396.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6980.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.79
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.15
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:01.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908117
  j =  2                              :            45940
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908292
  j =  2                              :            45845
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.20e-3
p-value of test                       :    0.9940

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.9932

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 2.79e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.35
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.83
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.23
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.64
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.02
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.89
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.57
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.39
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.76
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.42
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.75
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.61
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.79
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.74
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.88
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.04
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.14
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.53
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10016.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.02
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.96
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.77
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.85
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000045808

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.02
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999888584

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    2.68
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:07.47

 All tests were passed




Server wird beendet - Lösche Semaphor 51347481.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.51
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.34
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.50
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1488.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:06.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:56.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908623
  j =  2                              :            45687
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.78e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.09
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17341.78
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.84
p-value of test                       :    0.9917


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.60
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.06
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.26
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.62
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.79
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.50
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.46
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.52
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.60
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.11
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.90
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.36
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.66
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.85
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.93e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.46
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:59.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.47
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4339.30
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12099.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11860.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.44
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999979691

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.85
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999979355

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.41
p-value of test                       :    0.9919

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:21.30

 All tests were passed




Server wird beendet - Lösche Semaphor 52363289.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:48.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7499
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.11
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.00
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:00.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908015
  j =  2                              :            45985
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908446
  j =  2                              :            45774
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:31.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.52
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.81
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.80
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.75
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.96e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   16.76
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.25
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.95
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.53
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.04
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.33
p-value of test                       :    0.9970


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.06
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.77
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.40
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.02
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.46
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.34
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.98
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.72
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.40
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.52
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.69e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.38
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.59
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.86
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11610.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11694.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.64
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000050869

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.06
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999952310

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Tests on the sum of all N observations
Standardized normal statistic         :  -0.040
p-value of test                       :    0.52

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:01.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 67  MatrixRank, L=30, r=26          0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53411865.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1223
p-value of test                       : 1 -  5.3e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334343
  j =  1                              :        599997554
  j =  2                              :             1223
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    2.60
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.28
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.07
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.37
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.99
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  469.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.59
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.11
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908343
  j =  2                              :            45818
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45732
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869732
  j =  1                              :        399908537
  j =  2                              :            45730
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.77
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17539.34
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.69
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.37
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.90
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.55
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.75
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.12
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.72
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.09
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.43
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.32
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4829.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.03
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.64
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.03
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.02
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.12
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.77
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11546.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.32
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000035305

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.97
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999920522

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:06.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21          1 -  5.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54427673.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7061
p-value of test                       :    0.9987


-----------------------------------------------
CPU time used                    :  00:04:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.85
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.88
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.93
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.52
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1356.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.47
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.06
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4964.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46023
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870023
  j =  1                              :        399907955
  j =  2                              :            46021
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908377
  j =  2                              :            45807
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.16e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.17
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.33
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.66
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.40
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.67
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.69
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.05
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.62
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.69
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.05
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.79
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.35
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.97
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.47
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.72
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.05
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    5.25
p-value of test                       :  2.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.91
p-value of test                       :    0.9982

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.72e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.08
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.13
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.028
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.82
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4042.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3951.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11526.80
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.94
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999965309

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.25
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999962510

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.020
p-value of test                       :    0.49

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :  -0.033
p-value of test                       :    0.51

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:56.03

 All tests were passed




Server wird beendet - Lösche Semaphor 55476249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.41

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5255
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.91
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.52
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.63
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.60
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.11
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.07
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.51
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.62e-4
p-value of test                       :    0.9994    *****

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.54
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:03.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45526
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869526
  j =  1                              :        399908954
  j =  2                              :            45514
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907842
  j =  2                              :            46076
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:20.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.55e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.6e-3

Anderson-Darling statistic = A2       :    4.78
p-value of test                       :  3.7e-3


-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.08
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.78
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.88
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.24
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.37
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.54
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.67
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.54
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.92
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.28
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.48
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.99
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.30
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.45
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.74
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.17
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.65
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.88
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.62
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.32
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.64
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4322.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.27
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999986297

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.88
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000002671

Normal statistic for number of bits   :   0.021
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.93

 All tests were passed




Server wird beendet - Lösche Semaphor 56492057.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4451
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:44.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.23
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   90.57
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.20
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.16
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   38.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.03
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.38
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:57.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907804
  j =  2                              :            46095
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907740
  j =  2                              :            46127
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:32.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.45e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.62
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17313.89
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.08
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.42
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.47
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.52
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.25
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.94
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.22
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.53
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.22
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.53
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.93
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.60e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.76e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.74
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.42
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9685.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:20.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:57.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4803.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4342.61
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.37
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999949532

Normal statistic for number of bits   :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.74
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000086998

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.23
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :  -0.039
p-value of test                       :    0.52

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:40.86

 All tests were passed




Server wird beendet - Lösche Semaphor 57540633.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.74

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:06.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:42.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.17
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.08
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.08
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.18
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.78
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45648
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869648
  j =  1                              :        399908709
  j =  2                              :            45638
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907766
  j =  2                              :            46108
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.75e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.06e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.55
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.31
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.097
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.82
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.49
p-value of test                       :  5.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.82
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.00
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.29
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.58
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.42
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.11
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.67
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.47
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.98
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.21
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.14
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.42
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.47
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   39.00
p-value of test                       :  9.1e-3



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.82
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.93
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9831.09
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.91
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.90
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11537.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.61
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999821294

Normal statistic for number of bits   :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.79
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999903740

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:12.43

 All tests were passed




Server wird beendet - Lösche Semaphor 58621977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:48.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:11.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.25
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:46.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.84
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:21.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.83
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.27
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46220
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870220
  j =  1                              :        399907562
  j =  2                              :            46216
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907745
  j =  2                              :            46123
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.7e-3

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.24e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 1.89e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.07
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.94
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.66
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17217.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.86
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.47
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.99
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.63
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.84
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.05
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.13
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4910.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.19
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.06
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5150.74
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.55
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.44
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.44
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.07
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.00
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.99
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:00.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.61
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.97
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000054412

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.74
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000065368

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:44.31

 All tests were passed




Server wird beendet - Lösche Semaphor 59605017.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:13.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.46
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:49.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.28
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.97
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.82
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.98
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.71
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5188.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907414
  j =  2                              :            46284
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908187
  j =  2                              :            45899
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 3.31e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.73e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:10.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.67
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.64
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.65
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.16
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.83
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.40
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.76
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.02
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.25
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.22
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.45
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.86
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.17
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.50
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.87
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4870.11
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.98
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.69
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.17
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.51
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    1.81
p-value of test                       :    0.9996    *****


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.74
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 2.66e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.16
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.44
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.50
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -5.11e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.9935

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.46
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11827.74
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.58
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999963410

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.09
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999813131

Normal statistic for number of bits   :   -1.48
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:35.56
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60719129.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.72
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.57
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.10
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.49
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5263.46
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:57.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907832
  j =  2                              :            46081
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907970
  j =  2                              :            46012
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.01
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.39
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17125.67
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.83
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.31
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.43
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.16
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.42
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.36
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.06
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.17
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.74
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.33
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.70
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.29
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.98
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.44
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.12
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.04
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.88
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.19e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4654.31
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.37
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000106381

Normal statistic for number of bits   :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.64
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000104425

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.17
p-value of test                       :    0.9971

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:49.02

 All tests were passed




Server wird beendet - Lösche Semaphor 61734937.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5557
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     634
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.86
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.64
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.89
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.51
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.67
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:01.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908074
  j =  2                              :            45957
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.82e-3
p-value of test                       :    0.9960

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.24
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17354.93
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.79
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.38
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:34.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.66
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:34.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.59
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.73
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.34
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.84
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.83
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.86
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.96
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:33.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.19
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.79
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.61
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.73
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.84
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.00
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:13.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.89
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.49e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.96
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.22
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.91
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.72
p-value of test                       :    0.9903


-----------------------------------------------
Total number of bits:  7999976046

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.66
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999971933

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.03e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:14.52

 All tests were passed




Server wird beendet - Lösche Semaphor 62750745.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:00.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.31
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9965


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:10.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.07
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.48
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.59
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1388.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.82
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.20
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.50
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45926
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869926
  j =  1                              :        399908151
  j =  2                              :            45920
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908280
  j =  2                              :            45854
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.54
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.19
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.96
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.01
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.48
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.36
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.60
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.81
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.37
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   43.35
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:48.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.44
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:47.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.55
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4863.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.26
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.21
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.57
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.33
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.83
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.68
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.34
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:14.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.29e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.51
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.56
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:20.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.90
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11629.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.43
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000045547

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000142105

Normal statistic for number of bits   :    1.12
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:19:34.73

 All tests were passed




Server wird beendet - Lösche Semaphor 42795034.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:41.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1468
p-value of test                       :  2.8e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334588
  j =  1                              :        599997064
  j =  2                              :             1468
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9954

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:39.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.37
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.78
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7153.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.39
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.16
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.12
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.50
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908339
  j =  2                              :            45826
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908167
  j =  2                              :            45903
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.08
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.20
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.10
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.42
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.17
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.93
p-value of test                       :    0.9914


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.78
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.86
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.31
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.74
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.70
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.31
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.22
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.68
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.98
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.53
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.66
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.88
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.16
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.44
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:22.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.62
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.85
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999933944

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.78
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999957596

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:55.03

 All tests were passed




Server wird beendet - Lösche Semaphor 43122714.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4439
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:12.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:39.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    4.82
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.28
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.86
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.59
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.87
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5066.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907926
  j =  2                              :            46025
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908050
  j =  2                              :            45972
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:22.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.63e-4
p-value of test                       :  5.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.17e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.32
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.13
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.76
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.42
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17224.94
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.27
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   42.31
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.70
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.98
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.22
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.66
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.87
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.02
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.05
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.10
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.19
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.31
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.69
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 6.27e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.28
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.31
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.61
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.19
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.62
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000134584

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.19
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000053512

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:04.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 29  SimpPoker, r = 25               0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44138522.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.7e-3


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.58
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.47
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.51
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:40.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.16
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7197.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.04
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4872.43
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45536
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869536
  j =  1                              :        399908931
  j =  2                              :            45530
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908121
  j =  2                              :            45932
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:33.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    4.44
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.51e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.34
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.00
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.32
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17660.46
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.01
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.27
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.21
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.36
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.61
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.41
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.29
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.66
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.82
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.53
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.91
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.48
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.92e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.12
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.21
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.7e-4    *****

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5109.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.90
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12082.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.87
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999967550

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999978350

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    2.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:48.37

 All tests were passed




Server wird beendet - Lösche Semaphor 45121562.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.17
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9918

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     554
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.92
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.81
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    4.25
p-value of test                       :  6.6e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.42
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7164.24
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.02
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.28
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.06
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46085
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870085
  j =  1                              :        399907832
  j =  2                              :            46081
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45422
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869422
  j =  1                              :        399909161
  j =  2                              :            45412
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   14.68
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.22
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.46
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.22
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.29
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.56
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.69
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.18
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5091.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.38
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.34
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.87
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.84
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.59
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.52
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.92e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.66
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.29
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.01
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.51
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4718.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4199.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12177.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.65
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999975518

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.22
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999911618

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   0.024
p-value of test                       :    0.49

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:32.95

 All tests were passed




Server wird beendet - Lösche Semaphor 46170138.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5475
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.68
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.12
p-value of test                       :    0.9998    *****

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.69
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.27
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:54.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.31
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.95
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.64
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.07
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.21
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:57.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907944
  j =  2                              :            46025
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.72e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.92e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 9.50e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:28.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.95
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17430.09
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.66
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.98
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.05
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.00
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.55
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.76
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.43
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.73
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.78
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.67
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.54
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.50
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.25
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.67
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.20
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.89
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4997.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.29
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.31
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.60
p-value of test                       :    0.9910

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.09
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000043039

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.21
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999935426

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.072
p-value of test                       :    0.47

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:34.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.057
p-value of test                       :    0.52

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2, t = 5          0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47284250.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5295
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.15
p-value of test                       :  2.5e-3

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.87
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.06
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.25
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  365.31
p-value of test                       :    0.9927

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6886.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:16.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.60
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.46
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.38
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908464
  j =  2                              :            45765
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908580
  j =  2                              :            45710
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.03e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.68
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.39
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.94
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.77
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.78
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.06
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.42
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.79
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.23
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.45
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.64
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.07
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.24
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.49
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.22
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  440.80
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.73
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.64e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.69e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.58
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.57
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.40
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.42
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999906611

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.51
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000005473

Normal statistic for number of bits   :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:07.29

 All tests were passed




Server wird beendet - Lösche Semaphor 48332826.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.69
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.82
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7199.70
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.99
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.24
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.74
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46526
p-value of test                       :  1.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870526
  j =  1                              :        399906950
  j =  2                              :            46522
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46129
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870129
  j =  1                              :        399907746
  j =  2                              :            46121
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 6.19e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.36
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.25
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17436.27
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.88
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.93
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.84
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.86
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.36
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.31
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.47
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4854.26
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.84
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.04
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.19
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.52
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.92
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    2.43
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   22.45
p-value of test                       :  4.1e-3

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.92
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:34.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4867.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.65
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.50
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11880.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:34.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.32
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000005653

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.42
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000027730

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:32.27

 All tests were passed




Server wird beendet - Lösche Semaphor 49578010.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    3.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.24
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.35
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6793.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.51
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.91
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:40.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4978.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:19.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908094
  j =  2                              :            45947
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:32.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.19
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.15
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.59
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.31
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.98
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.67
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.55
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.11
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.43
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.14
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.52
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.89
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.89
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.84
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.78
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.42
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 5.06e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.82
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4776.21
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11613.79
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:33.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.48
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000110443

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.08
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999955232

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.3e-3

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:35.79

 All tests were passed




Server wird beendet - Lösche Semaphor 50790426.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:11.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:15.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    2.20
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     326
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.97
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.26
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.87
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:48.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.50
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5114.80
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908626
  j =  2                              :            45681
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45817
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869817
  j =  1                              :        399908370
  j =  2                              :            45809
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:31.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 9.79e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.016
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.77
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.71
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.68
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.58
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.57
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.85
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.08
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.83
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.46
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.50
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.37
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5145.21
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  459.77
p-value of test                       :  2.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  476.29
p-value of test                       :  9.1e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5192.29
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.59
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.00
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.14
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.59e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.44
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.71
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.40
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.36
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.45
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000035737

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.96
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999953027

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:30.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   9.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52133914.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:42.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:47.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.07
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.56
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.27
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.85
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.99
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:56.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908200
  j =  2                              :            45894
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45679
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869679
  j =  1                              :        399908644
  j =  2                              :            45675
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.4e-3

Kolmogorov-Smirnov- statistic = D-    : 8.92e-4
p-value of test                       :    0.9991    *****

Anderson-Darling statistic = A2       :    5.00
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.51e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.75
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.79
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.63
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.34
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17217.56
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.06
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.48
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.69
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.13
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.15
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.12
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.67
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.47
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.90
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.37
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.22
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.98
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5201.85
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.86
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.14
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.63
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.81
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.96
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.93
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   41.00
p-value of test                       :  2.3e-3



-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.65
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.54
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9834.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.85
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4036.16
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11475.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.50
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000118288

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.55
p-value of test                       :  9.1e-3


-----------------------------------------------
Total number of bits:  7999795812

Normal statistic for number of bits   :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:13.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft, t = 8                   0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53313562.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:17.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    3.53
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.99
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.69
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1536.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7281.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.71
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.64
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.14
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.66
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.15
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908388
  j =  2                              :            45806
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908027
  j =  2                              :            45979
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.71e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.40
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.83
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.99
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.45
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.12
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.60
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.77
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.60
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.36
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.52
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.64
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.35
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.85
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5194.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.63
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.46
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.42
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.64
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.07e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.86
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.72
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.63
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.60
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.21
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:04:18.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11909.91
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11961.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.85
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999931922

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.30
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999898883

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9923

Tests on the sum of all N observations
Standardized normal statistic         :   0.041
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:43.38

 All tests were passed




Server wird beendet - Lösche Semaphor 54296602.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.35
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    2.08
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.98
p-value of test                       :  3.3e-3

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6817.29
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4926.96
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46268
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870268
  j =  1                              :        399907466
  j =  2                              :            46264
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908588
  j =  2                              :            45703
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 2.99e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.46e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.03e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.07e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.94
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17039.28
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.87
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.60
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.48
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.48
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.00
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.22
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.82
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.45
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.01
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.61
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.69
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.27
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.79
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.93
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.56
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.62
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.97
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.06
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.27
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.67
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.07
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000146626

Normal statistic for number of bits   :    1.16
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.00
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000090307

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:20.17

 All tests were passed




Server wird beendet - Lösche Semaphor 55345178.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.76
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    3.02
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    3.47
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.68
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.37
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.21
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1487.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7226.55
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.56
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.99
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45826
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869826
  j =  1                              :        399908353
  j =  2                              :            45816
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45705
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869705
  j =  1                              :        399908596
  j =  2                              :            45693
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  6.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  2.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.31
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.06
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.04
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.82
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:55.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.92
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.53
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.87
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.70
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.86
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.92
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.81
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.98
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.78
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.16
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.55
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.94
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.11
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.61
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.62
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.66
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.01
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.01
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.33
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.07
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.48
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.82
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10219.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.19
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5028.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11794.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.80
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999931016

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.70
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000164125

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.25
p-value of test                       :    0.01

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:51.87

 All tests were passed




Server wird beendet - Lösche Semaphor 56328218.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1241
p-value of test                       :    0.9996    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334361
  j =  1                              :        599997518
  j =  2                              :             1241
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4239
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:04:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9935


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.21
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  198.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  388.11
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7251.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.16
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.44
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5122.93
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45474
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869474
  j =  1                              :        399909055
  j =  2                              :            45468
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908323
  j =  2                              :            45834
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.61e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.72e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.64
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.37
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.10
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.73
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.4e-3

Kolmogorov-Smirnov- statistic = D-    : 4.00e-3
p-value of test                       :    0.9959

Anderson-Darling statistic = A2       :    4.08
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   96.73
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17577.68
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.63
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.54
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.30
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.33
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.90
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.63
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.58
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.78
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.95
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.60
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.92
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.71
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.70
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.20
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.52
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.80
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.31
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.00
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11772.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.73
p-value of test                       :  8.8e-3


-----------------------------------------------
Total number of bits:  8000132199

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.68
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000073387

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57344026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     646
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    3.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.73
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.58
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.27
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.14
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7072.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.15
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.63
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:58.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45883
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869883
  j =  1                              :        399908238
  j =  2                              :            45875
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45889
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869889
  j =  1                              :        399908226
  j =  2                              :            45881
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.18
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.71
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17721.85
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.62
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.43
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.30
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.14
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.59
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  183.21
p-value of test                       :  4.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.75
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.55
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.97
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.25
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.61
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.09
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.54
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.77
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.20
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.13
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    2.36
p-value of test                       :  9.0e-3



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.88e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.66
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.9911

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10246.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4751.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4231.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11758.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.89
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000113134

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.05
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000045847

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:48.84

 All tests were passed




Server wird beendet - Lösche Semaphor 58327066.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     551
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    2.11
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.51
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.11
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.11
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.71
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.73
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45739
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869739
  j =  1                              :        399908526
  j =  2                              :            45731
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45731
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869731
  j =  1                              :        399908541
  j =  2                              :            45725
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.24e-3
p-value of test                       :    0.9954

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.23e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.38
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.50
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17353.93
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.42
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.28
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.73
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.45
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.20
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.92
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.86
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.40
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.85
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.75
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.93
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.85
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.88
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.64
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.04
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.92
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.37
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.84e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.67
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11893.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11512.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.13
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000031801

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.48
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999986057

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.14

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:31.87

 All tests were passed




Server wird beendet - Lösche Semaphor 59310106.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1246
p-value of test                       :    0.9994    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334366
  j =  1                              :        599997508
  j =  2                              :             1246
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.06
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:19.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:51.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.65
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.49
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.96
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.91
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.70
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.28
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.26
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:55.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908550
  j =  2                              :            45722
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45303
p-value of test                       :    0.9965


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869303
  j =  1                              :        399909395
  j =  2                              :            45301
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.77
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.87
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17608.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.11
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.94
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.74
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.54
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.88
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.73
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.48
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.47
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.54
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.49
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4765.61
p-value of test                       :    0.9912


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.90
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.93
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.20
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    2.51
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.52e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.41e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10293.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.084
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4962.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11564.08
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.90
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000031225

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.85
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999898949

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:24.86
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60293146.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5518
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4473
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:12.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.13
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.26
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.68
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.29
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.08
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1547.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6825.41
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.00
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5219.19
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:03:01.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45589
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869589
  j =  1                              :        399908824
  j =  2                              :            45585
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45997
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869997
  j =  1                              :        399908007
  j =  2                              :            45995
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:33.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.82
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.69
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17224.30
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.85
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.67
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.81
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.01
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.51
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.36
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.93
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.93
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.16
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.98
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.88
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  426.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.65
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.99
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    2.42
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.21e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.08
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.19
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-3
p-value of test                       :    0.9974

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.4e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.52
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9773.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:34.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4926.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5000.19
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11878.94
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.73
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.88
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000053749

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.86
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999992165

Normal statistic for number of bits   :  -0.062
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.89
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.93
p-value of test                       :    0.97

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:03.59

 All tests were passed




Server wird beendet - Lösche Semaphor 61341722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4172
p-value of test                       :    0.9939


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:15.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.09
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.86
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4998.78
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908410
  j =  2                              :            45789
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908204
  j =  2                              :            45898
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.62
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.05
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.03
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17793.97
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.00
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.24
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.43
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.49
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.38
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.29
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.21
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  176.37
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5147.56
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.58
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.98
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.18
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.87
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.67
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.68
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   0.016
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.92e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.50e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.26
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.12
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9937.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:50.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.43
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.91
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.57
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000034294

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.73
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000001354

Normal statistic for number of bits   :   0.011
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:08.01

 All tests were passed




Server wird beendet - Lösche Semaphor 62455834.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:10.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    4.20
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.37
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  182.34
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.58
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1518.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.56
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.57
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.45
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.47
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45751
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869751
  j =  1                              :        399908502
  j =  2                              :            45743
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908109
  j =  2                              :            45941
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:32.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.69e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.90
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:34.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17590.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.03
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.69
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.75
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:34.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.78
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.49
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.65
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.56
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.80
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.99
p-value of test                       :  3.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.72
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.93
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.97
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.46
p-value of test                       :    0.9900


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.29
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.54
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.26
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.97
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.16
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.91e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.12
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.98
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11677.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.45
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000175333

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.80
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999869492

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:27.23

 All tests were passed




Server wird beendet - Lösche Semaphor 42827803.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5392
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.91
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.82
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6752.86
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.44
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.10
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.90
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.63
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908389
  j =  2                              :            45798
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45944
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869944
  j =  1                              :        399908115
  j =  2                              :            45938
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.25e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17159.31
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.99
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.65
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.82
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.66
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.83
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.11
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.10
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.37
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.69
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.21
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.78
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.33e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.63
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.85
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:10.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.50
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12098.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999973331

Normal statistic for number of bits   :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000075562

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:42.09

 All tests were passed




Server wird beendet - Lösche Semaphor 43843611.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  8.2e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:54.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.81
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908144
  j =  2                              :            45925
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46222
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870222
  j =  1                              :        399907557
  j =  2                              :            46220
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.12
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.99
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.77
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.64
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.86
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.76
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.67
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.19
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.61
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.19
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.57
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.74
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.83
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.69
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5078.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.97
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.71
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.39
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.02
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:20.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.19
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.02
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11877.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:34.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11595.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.00
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999889229

Normal statistic for number of bits   :   -0.88
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.25
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  8000055321

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:09.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  2  SerialOver, r = 22              8.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44630043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1474
p-value of test                       :  1.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334594
  j =  1                              :        599997052
  j =  2                              :             1474
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7497
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.72
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     650
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.98
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     336
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:33.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6990.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.49
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.07
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:26.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908401
  j =  2                              :            45798
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45952
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869952
  j =  1                              :        399908097
  j =  2                              :            45950
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9949


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.48e-4
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    5.06
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.41
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.75
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.72
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.41
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.74
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.58
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.28
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.63
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.44
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.03
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.24
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.78
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.62
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.57
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.48
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.44
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.24
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5233.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.72
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.87
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.92
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.56e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.44
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9792.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9806.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.43
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.86
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.95
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999988232

Normal statistic for number of bits   :  -0.093
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.30
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999975752

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.64
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:44.35

 All tests were passed




Server wird beendet - Lösche Semaphor 45547547.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1545
p-value of test                       :  8.6e-7    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334665
  j =  1                              :        599996910
  j =  2                              :             1545
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7545
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.60
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.83
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.17
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.09
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7366.45
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:10.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5094.11
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908287
  j =  2                              :            45849
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908184
  j =  2                              :            45902
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.06e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.09e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.027
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.97
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.68
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.18
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.56
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.95
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.89
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.42
p-value of test                       :  1.0e-2


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.58
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.83
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.31
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.01
p-value of test                       :    0.9939


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5215.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.85
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.24
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.74
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.13
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.25
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -2.12
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.21e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.53
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.30
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.14
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.91
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.90
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12127.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.03
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999768803

Normal statistic for number of bits   :   -1.83
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.13
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999937271

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.63
p-value of test                       :    0.9958

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:27.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           8.6e-7
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46366747.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:51.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.38
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.54
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.93
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.82
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.10
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.16
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.84
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.12
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.06
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:57.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45914
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869914
  j =  1                              :        399908177
  j =  2                              :            45904
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908738
  j =  2                              :            45622
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.01e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-5
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.57
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.46
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.99
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.06
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.56
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.96
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.34
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.96
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.76
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.92
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.22
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.50
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.42
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.99
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.21
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.14
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.68e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.70
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.95
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.83
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10321.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:04:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.30
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11500.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.81
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.77
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999955178

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.01
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000045589

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:37.29

 All tests were passed




Server wird beendet - Lösche Semaphor 47382555.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.17
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.37
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  292.99
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1528.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7165.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.92
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908100
  j =  2                              :            45947
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908227
  j =  2                              :            45885
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.74
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.76
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   45.25
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.55
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.40
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.70
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.81
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.20
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.36
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.85
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.76
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.05
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.22
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.18
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.24
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.04
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4940.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.01
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    2.21
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.43e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.18
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:21.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.20
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12175.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.94
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000052180

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.34
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999990233

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.62

 All tests were passed




Server wird beendet - Lösche Semaphor 48398363.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7481
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:37.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.43
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.86
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.20
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:15.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.11
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5132.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:56.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46033
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870033
  j =  1                              :        399907936
  j =  2                              :            46029
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907983
  j =  2                              :            46001
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.9948

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.88
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.68
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.46
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.95
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.49
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.62
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.49
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.78
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.11
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.01
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.00
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  148.12
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.22
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.41
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.37
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.06e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9936.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:34.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.30
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000055603

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.24
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000171955

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:28.45

 All tests were passed




Server wird beendet - Lösche Semaphor 49414171.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:40.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4526
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.74
p-value of test                       :  4.1e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    5.79
p-value of test                       :  1.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     349
p-value of test                       :  3.1e-3

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.80
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.12
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.09
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.07
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.18
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908672
  j =  2                              :            45652
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907729
  j =  2                              :            46131
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.78e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.23
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  165.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.57
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.76
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.72
p-value of test                       :    0.9942


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.18
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.83
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.12
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.40
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.39
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.90
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.28
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.17
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  167.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.57
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.14
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5191.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.18
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.68
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.11
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.35
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.55
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.02e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.05
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.83
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.15
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.31e-3
p-value of test                       :    0.9933

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9759.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.31
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:20.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.45
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000021364

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.11
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000039472

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:05.59

 All tests were passed




Server wird beendet - Lösche Semaphor 50593819.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5366
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7599
p-value of test                       :  5.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.30
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    3.79
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    5.02
p-value of test                       :  2.8e-3

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.94
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.69
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7067.03
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:47.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.69
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.96
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:54.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45963
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869963
  j =  1                              :        399908076
  j =  2                              :            45959
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908049
  j =  2                              :            45971
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :  8.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.60e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.95
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.61
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17560.59
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.11
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.25
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.89
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.29
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.67
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.68
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.85
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.05
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.53
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.14
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.06
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.36
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.95
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.45
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.51e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.89e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10084.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10168.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4711.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:33.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11635.55
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.24
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000114043

Normal statistic for number of bits   :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.01
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000102004

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.62
p-value of test                       :  1.7e-4    *****

Anderson-Darling statistic = A2       :    6.46
p-value of test                       :  6.5e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    2.97
p-value of test                       :  1.5e-3

Sample variance                       :    0.16
p-value of test                       :    0.9976

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:10.20
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        5.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51576859.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    3.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.12
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.75
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1513.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.87
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.09
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:08.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.82
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.75
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45724
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869724
  j =  1                              :        399908556
  j =  2                              :            45716
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908222
  j =  2                              :            45883
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:30.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.67e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.02e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.65e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.79
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.46
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.79
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.54
p-value of test                       :  3.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.75
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.83
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.20
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.76
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   92.06
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.57
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.48
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.92
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.04
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.43
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   0.057
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.10
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.93
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9908.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11820.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11483.41
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.35
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999982391

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.34
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999989120

Normal statistic for number of bits   :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.88
p-value of test                       :    0.03

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.92

 All tests were passed




Server wird beendet - Lösche Semaphor 52756507.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5526
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.70
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.18
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.78
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6859.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.33
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.80
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907809
  j =  2                              :            46091
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908093
  j =  2                              :            45943
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:30.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.91
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.24e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.66
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.88
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17307.39
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.81
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.93
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.67
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.37
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.20
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.46
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.80
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.84
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.23
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.94
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.68
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.77
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.84
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.56
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.69
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.17
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.81e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.72
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.45
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.41
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4659.47
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.58
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11465.90
p-value of test                       :    0.9907

-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.25
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000041203

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.66
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999995021

Normal statistic for number of bits   :  -0.039
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:12.88

 All tests were passed




Server wird beendet - Lösche Semaphor 53805083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7085
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.03
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.05
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.82
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.20
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.19
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.06
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:27.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4995.49
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908619
  j =  2                              :            45683
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46092
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870092
  j =  1                              :        399907818
  j =  2                              :            46088
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:30.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-5
p-value of test                       :    0.9955

Kolmogorov-Smirnov- statistic = D-    : 2.96e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.90e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.57
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.56
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  584.09
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.22
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.58
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.61
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.38
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.24
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.66
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.59
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.89
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.79
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.52
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :    1.96
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.38e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.96
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.64
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.19
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.73
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12191.43
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.05
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.30
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000131206

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.64
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999869393

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.041
p-value of test                       :    0.52

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:45.22

 All tests were passed




Server wird beendet - Lösche Semaphor 54853659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9915


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:12.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    2.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:47.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.33
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.22
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.07
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:21.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4836.28
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908283
  j =  2                              :            45854
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45416
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869416
  j =  1                              :        399909171
  j =  2                              :            45410
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.09e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.13e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.99
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.13
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.37
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.95
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.62
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.54
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  182.00
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  579.61
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.04
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.93
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.03
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  262.41
p-value of test                       :  2.0e-3


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  488.58
p-value of test                       :  2.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.43
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4696.81
p-value of test                       :    0.9990


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.05
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4160.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11633.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11409.41
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.39
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000097882

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   77.21
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000068602

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:05.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 H (L=10000, r=15)   2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55869467.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.74
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.87
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.85
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7157.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.59
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.38
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5176.53
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908079
  j =  2                              :            45950
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908255
  j =  2                              :            45865
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.82e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.75e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.67
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.76
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.80
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.17
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17409.79
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.97
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.18
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.76
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.26
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.56
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.55
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.18
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.56
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.56
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.64
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.37
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.74
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.44
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.84
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.21
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.71
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    2.56
p-value of test                       :  5.3e-3



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.11e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.25e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.56
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.58
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.73
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:20.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.67
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5076.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11836.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:33.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11662.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.09
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000048895

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.55
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999844172

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:34.04

 All tests were passed




Server wird beendet - Lösche Semaphor 57016347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4221
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7422
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:10.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:13.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    2.75
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:20.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.33
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.97
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.33
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.82
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.17
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.20
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:00.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907810
  j =  2                              :            46095
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907853
  j =  2                              :            46066
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.31e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17437.83
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.15
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.94
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.53
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.96
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.51
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.77
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.31
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.25
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.15
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.92
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.55
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.28
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.82
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.36e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:29.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.98
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12137.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.66
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.15
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999972641

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.93
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000001456

Normal statistic for number of bits   :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   0.025
p-value of test                       :    0.49

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:15.75

 All tests were passed




Server wird beendet - Lösche Semaphor 58032155.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5502
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:10.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:49.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.89
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.68
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:16.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.35
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.51
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45493
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869493
  j =  1                              :        399909015
  j =  2                              :            45491
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 4.52e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.55
p-value of test                       :    0.9918

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.96
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17257.59
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.15
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.73
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.83
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.46
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.23
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.12
p-value of test                       :  5.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.25
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.00
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.38
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.90
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.26
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.60
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.36
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.07
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.64e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.73e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.25
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.16
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10417.70
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9794.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:36.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.55
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11487.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.99
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000104992

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.30
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999983909

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         : -9.68e-3
p-value of test                       :    0.50

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:59.80

 All tests were passed




Server wird beendet - Lösche Semaphor 59179035.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5337
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4463
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9924


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     565
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1540.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6998.56
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:15.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.64
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907983
  j =  2                              :            46001
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46077
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870077
  j =  1                              :        399907847
  j =  2                              :            46075
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:29.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  5.9e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.9970

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.12e-5
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.13
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.34
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   73.84
p-value of test                       :  3.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.99
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.94
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.71
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.42
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.37
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.58
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.65
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.95
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.14
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.10
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.72
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.35
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.37
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.28
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.81
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.52
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.71
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.88
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.93e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 5.14e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.35
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.19
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.098
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:17.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5103.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.15
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999948638

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.87
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999891335

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.02
p-value of test                       :    0.98

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:11.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 64  WeightDistrib, r = 26           3.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60325915.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.15
p-value of test                       :    0.9989


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.71
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.76
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.83
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.20
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5107.82
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:00.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908548
  j =  2                              :            45726
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46307
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870307
  j =  1                              :        399907391
  j =  2                              :            46297
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.54e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.23e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.96
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.85
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.38
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.89
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17699.08
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.90
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.73
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.81
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.81
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.53
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.65
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.17
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.51
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.41
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.66
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.67
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.23
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.88
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.68
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.64
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 5.07e-3
p-value of test                       :    0.9947

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.79
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12074.94
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.71
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000010432

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.76
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000099091

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:37.01

 All tests were passed




Server wird beendet - Lösche Semaphor 61276187.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:09.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.91
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.82
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.19
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.72
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.69
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:03.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45434
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869434
  j =  1                              :        399909132
  j =  2                              :            45434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46339
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870339
  j =  1                              :        399907324
  j =  2                              :            46335
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.59
p-value of test                       :  4.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9984


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.13e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 3.63e-4
p-value of test                       :  5.2e-3

Anderson-Darling statistic = A2       :    4.64
p-value of test                       :  4.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 7.94e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.12
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.60
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17264.91
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.38
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.37
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.19
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.08
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.22
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.37
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.73
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.02
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.87
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.74
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.57
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   42.54
p-value of test                       :    0.9988


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.78
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.85
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.90
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.14
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.36
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    2.82
p-value of test                       :  2.4e-3



-----------------------------------------------
CPU time used                    :  00:02:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.31e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.71
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.20
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.82
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.52
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.80
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000059959

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.57
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000008164

Normal statistic for number of bits   :   0.065
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:37.45

 All tests were passed




Server wird beendet - Lösche Semaphor 62291995.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5311
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.21
p-value of test                       :  2.4e-3

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     557
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.54
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    3.63
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  384.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7215.80
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.35
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4894.73
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:01.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908415
  j =  2                              :            45785
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908641
  j =  2                              :            45678
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.87e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.021
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:41.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.67
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.09
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.37
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17481.03
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:54.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   36.79
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.30
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.68
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.56
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.23
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.44
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.56
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.77
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.79
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.72
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.80
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.66
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.90
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:14.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.86e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 9.97e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   21.12
p-value of test                       :  6.8e-3

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5047.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.61
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.68
p-value of test                       :    0.9934


-----------------------------------------------
Total number of bits:  7999941768

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.64
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000061270

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    2.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:19:31.27

 All tests were passed




Server wird beendet - Lösche Semaphor 42860572.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5373
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7187
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4204
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.10
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.54
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.98
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908633
  j =  2                              :            45676
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908400
  j =  2                              :            45794
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.72e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.50e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.08e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.054
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17874.76
p-value of test                       :  9.0e-3



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.27
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.96
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.35
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.42
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.93
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  413.78
p-value of test                       :    0.9980


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.11
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.52
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4856.02
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.32
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.70
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.04
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.25
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.60
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.13
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10204.52
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.039
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.11
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.06
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000041416

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000009574

Normal statistic for number of bits   :   0.076
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:09.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:58.37

 All tests were passed




Server wird beendet - Lösche Semaphor 43089948.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7489
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.70
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  187.72
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.59
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6806.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.93
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5271.57
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908430
  j =  2                              :            45785
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908526
  j =  2                              :            45728
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.94e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.25e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.16
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   50.53
p-value of test                       :  1.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.78
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.99
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.68
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.54
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5175.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.77
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.69
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.65
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.89
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:28.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.03
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9913

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.21e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.62
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.05
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.084
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.20
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4933.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.71
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4068.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.46
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000100558

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   34.17
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000005563

Normal statistic for number of bits   :   0.044
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.061
p-value of test                       :    0.52

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:13.62

 All tests were passed




Server wird beendet - Lösche Semaphor 44105756.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5524
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:48.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7173
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:05.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:09.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    4.53
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.97
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.05
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7094.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.33
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.24
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.08
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.00
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:40.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.68
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45843
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869843
  j =  1                              :        399908319
  j =  2                              :            45833
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46226
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870226
  j =  1                              :        399907551
  j =  2                              :            46220
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.96e-3
p-value of test                       :    0.9907

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:07.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:20.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.68e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.26e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.94
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.40
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17314.20
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.35
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.87
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.43
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.47
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.86
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.45
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.38
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.64
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.55
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.34
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.30
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.89
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.94
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 6.08e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.32
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:34.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.51
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10173.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.06
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.93
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4007.12
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.96
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000054856

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.10
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000077698

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.54
p-value of test                       :    0.9945

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.91
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:41.77
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 85  Fourier3, r = 27                0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45154332.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:41.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5441
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9902

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.09
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.31
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.05
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7066.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.26
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:17.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.14
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.47
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.18
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45848
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869848
  j =  1                              :        399908306
  j =  2                              :            45844
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:32.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:20.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.55e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.01
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.41
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17603.78
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.24
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.51
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.87
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.97
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.99
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.30
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.43
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.29
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.69
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.63
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.88
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.19
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4849.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.86
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.40
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.45
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.48e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 9.23e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.41
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.65
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.36
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.45
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:59.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.86
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.83
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000108247

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.70
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999897617

Normal statistic for number of bits   :   -0.81
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Tests on the sum of all N observations
Standardized normal statistic         :  -0.036
p-value of test                       :    0.51

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:49.67

 All tests were passed




Server wird beendet - Lösche Semaphor 46661660.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997329
  j =  2                              :             1334
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:54.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:30.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:31.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7540
p-value of test                       :  5.0e-3


-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:48.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.72
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.60
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.93
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6969.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:42.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.72
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.41
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.72
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:00.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908271
  j =  2                              :            45863
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907967
  j =  2                              :            46015
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:12.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 3.61e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.40
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17528.94
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.87
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.94
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.44
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.60
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.03
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.03
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.12
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.22
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.23
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.74
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.57
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.59
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.81
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.12
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.39
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.94
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.27e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.88
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.89
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5022.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.53
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.38
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.08
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:31.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.24
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999989306

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.88
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  8000096943

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:44.64

 All tests were passed




Server wird beendet - Lösche Semaphor 47906844.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5533
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    4.50
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  380.16
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6830.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.05
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.98
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907750
  j =  2                              :            46119
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907733
  j =  2                              :            46126
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.15e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.80
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17716.60
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.29
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.61
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.57
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.91
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.19
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.98
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.98
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.95
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.96
p-value of test                       :    0.9919


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.97
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.63
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.49
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.09
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.73
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.90
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.96
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.45
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.6e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4129.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12198.74
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.52
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000098071

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.65
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000133207

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.7e-4    *****

Anderson-Darling statistic = A2       :    4.81
p-value of test                       :  3.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.75
p-value of test                       :  3.0e-3

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.57

 All tests were passed




Server wird beendet - Lösche Semaphor 48791580.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5585
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:14.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:16.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     126
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.66
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.81
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.26
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.98
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5156.65
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46201
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870201
  j =  1                              :        399907599
  j =  2                              :            46199
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908311
  j =  2                              :            45840
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.62
p-value of test                       :  4.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:09.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:19.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.69e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.55
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.75
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   15.48
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17180.19
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   14.91
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.36
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.31
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.68
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.54
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.67
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.86
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.78
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.84
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.26
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.96
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.93
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.73
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.73
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.18
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.78
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.15
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.19e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  260.43
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.75
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10118.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.79
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.27
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4309.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.83
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.88
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999962519

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.21
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000071413

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         : 4.54e-3
p-value of test                       :    0.50

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:06.90

 All tests were passed




Server wird beendet - Lösche Semaphor 49774620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4202
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.65
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.41
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1525.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.65
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.23
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  166.97
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.83
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46104
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870104
  j =  1                              :        399907796
  j =  2                              :            46096
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46098
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870098
  j =  1                              :        399907809
  j =  2                              :            46088
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.70
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.12
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.62
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.12
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.34
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17435.31
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.12
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.12
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.04
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.84
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.40
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.33
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.48
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.38
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.16
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   44.05
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.28
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5193.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.28
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.01
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.31
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.09
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    2.14
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   0.043
p-value of test                       :    0.48

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.37e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.61
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.78
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.15
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9781.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9744.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.54
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.31
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4311.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.70
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000068779

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.81
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000023104

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.14
p-value of test                       :    0.02

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:41.19

 All tests were passed




Server wird beendet - Lösche Semaphor 51019804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.81
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.76
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.21
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.28
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.15
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:02.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46056
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870056
  j =  1                              :        399907888
  j =  2                              :            46056
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908343
  j =  2                              :            45821
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.41
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 4.25e-4
p-value of test                       :  7.3e-4    *****

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.5e-3

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.98e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.55
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.60
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.14
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.78
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.46
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   66.47
p-value of test                       :  1.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.98
p-value of test                       :  5.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.74
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.38
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.30
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.92
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.97
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.44
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.19
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.65
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.42
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.89
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.30
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.31
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.23
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.91e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 2.71e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.23
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.02
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:17.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.17
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3951.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12041.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.83
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999926810

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.31
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999951341

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:56.70

 All tests were passed




Server wird beendet - Lösche Semaphor 51937308.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5478
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    3.89
p-value of test                       :  9.9e-3

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     659
p-value of test                       :  9.2e-3

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.59
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.80
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.92
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.69
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    4.10
p-value of test                       :  8.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   51.72
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:21.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.67
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.72
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:02.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908861
  j =  2                              :            45559
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907667
  j =  2                              :            46162
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.94e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.017
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.43
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.07
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.48
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.79
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.12
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.21
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.27
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.05
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.03
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.13
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.93
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.14
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.38
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.15
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.57
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.71
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.79
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.23
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.23
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.36
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.52
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.10
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.57
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.27
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.73e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.22
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.76
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  243.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9860.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:32.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.04
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4252.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.85
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.41
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999962876

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.46
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999830267

Normal statistic for number of bits   :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:58.85

 All tests were passed




Server wird beendet - Lösche Semaphor 52920348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:48.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7163
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:11.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    2.29
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.99
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.36
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.52
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.40
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.65
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.71
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.43
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5208.14
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:56.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908225
  j =  2                              :            45880
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908251
  j =  2                              :            45873
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-3
p-value of test                       :    0.9990

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  3.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.96e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.47
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17533.88
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.98
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.11
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.31
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.07
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.34
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.14
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.49
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5075.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.55
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.37
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.42
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.30
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 2.82e-3
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 9.11e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.91
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.60
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.32
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10021.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3980.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11680.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.04
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000049927

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.77
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000020038

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.056
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:42.37

 All tests were passed




Server wird beendet - Lösche Semaphor 54394908.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:48.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1266
p-value of test                       :    0.9963

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334386
  j =  1                              :        599997468
  j =  2                              :             1266
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7124
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.58
p-value of test                       :  4.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.08
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.49
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.21
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.05
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.43
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:01.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908207
  j =  2                              :            45895
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908049
  j =  2                              :            45968
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9953


-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9900

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.64
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.91
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.67
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.33
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.98
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.37
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.13
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.56
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.56
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   99.13
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.85
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.11
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.05
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.36
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.53
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.27
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.39
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9755.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:52.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11589.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.75
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000062665

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.05
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000054622

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.19
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.1e-4    *****

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.44
p-value of test                       :  7.3e-3

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:36.61

 All tests were passed




Server wird beendet - Lösche Semaphor 55443484.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1476
p-value of test                       :  1.5e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334596
  j =  1                              :        599997048
  j =  2                              :             1476
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4196
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.45
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.97
p-value of test                       :  9.1e-3

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.68
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.77
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.06
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.71
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6985.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.51
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.80
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.26
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:00.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45601
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869601
  j =  1                              :        399908805
  j =  2                              :            45587
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46398
p-value of test                       :  7.9e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870398
  j =  1                              :        399907207
  j =  2                              :            46392
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.01e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:19.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.89
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.05
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.00
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.64
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.85
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.99
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.87
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.13
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.58
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.21
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.73
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.31
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.80
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.04
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.28
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.55
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.74
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.29
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.65
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.72
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.96
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   0.012
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.47
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.56
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:11.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.10
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4015.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12165.76
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.86
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999884195

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.27
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999850664

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:05.97

 All tests were passed




Server wird beendet - Lösche Semaphor 56459292.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.39
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.81
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.79
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.13
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.45
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.61
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908661
  j =  2                              :            45665
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907738
  j =  2                              :            46122
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951


-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.15e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.98
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.46
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.36
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.09
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17196.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.45
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.32
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.00
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.78
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.42
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.29
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.34
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.99
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.35
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.08
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.87
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  476.80
p-value of test                       :  8.6e-4    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.84
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  447.51
p-value of test                       :  7.9e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.99
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.81
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.97e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.97e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.66
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.32
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.64
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:04:12.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.49
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.82
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000117982

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.16
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000118765

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:44.61
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 M (L=10000, r=15)   8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57475100.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:48.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:10.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:15.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.62
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9938

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.96
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    3.00
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:14.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.66
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.84
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.57
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1531.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6847.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.08
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.45
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:42.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.45
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908032
  j =  2                              :            45984
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45925
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869925
  j =  1                              :        399908156
  j =  2                              :            45913
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:21.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-5
p-value of test                       :    0.9938

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.17
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17177.88
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.60
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.36
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.56
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.09
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.97
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.08
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.07
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  187.40
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.76
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.10
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.96
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.07
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.56
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.24
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.47
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.34
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.29
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5124.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.16
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 5.80e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.91
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.45
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.28
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.93
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5095.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11812.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.01
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999863447

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.06
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999997844

Normal statistic for number of bits   :  -0.017
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:29.59

 All tests were passed




Server wird beendet - Lösche Semaphor 58523676.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     952
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    4.72
p-value of test                       :  3.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    2.86
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.75
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.15
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.84
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.25
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  362.44
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6905.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.10
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.57
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.93
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:55.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46009
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870009
  j =  1                              :        399907987
  j =  2                              :            45999
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908130
  j =  2                              :            45932
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:34.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:11.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.31e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.62e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.56
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.092
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.33
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.63
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.71
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.70
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.06
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.22
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.33
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.16
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.95
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.49
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.31
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.06
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.20
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.95
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.69
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.06
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.23
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.41
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.17
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.01
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.10
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000157660

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.00
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999981299

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.010
p-value of test                       :    0.50

Sample variance                       :    1.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.94
p-value of test                       :  1.6e-3

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.77

 All tests were passed




Server wird beendet - Lösche Semaphor 59637788.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    6.61
p-value of test                       :  5.2e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:41.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:03.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.17
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.49
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.14
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:56.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908294
  j =  2                              :            45850
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46258
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870258
  j =  1                              :        399907487
  j =  2                              :            46252
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.49e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.51e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   96.17
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.92
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.35
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17522.07
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.46
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.84
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.79
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.44
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.90
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.69
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.71
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  436.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5227.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.36
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.19
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.28
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.24
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.27
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.82e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.71
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.13
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:10.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4667.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.10
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11510.02
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:29.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.81
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  7999986039

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.59
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000136501

Normal statistic for number of bits   :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    2.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:05.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          5.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60653596.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7477
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:15.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:20.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    3.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9909

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9926

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.78
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.90
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.64
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7180.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.56
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.88
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.93
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.06
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:58.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908192
  j =  2                              :            45901
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908415
  j =  2                              :            45785
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.37e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.07e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.9958

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 4.82e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:25.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.61
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.94
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.81
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.71
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.19
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.25
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.26
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.40
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5287.96
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.06
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.50
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.45
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5096.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  422.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.20
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:34.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.56
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.15e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.57
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.85
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.022
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:34.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.20
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:34.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.39
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999972422

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.28
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000069385

Normal statistic for number of bits   :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:15.62

 All tests were passed




Server wird beendet - Lösche Semaphor 61636636.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7515
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    3.12
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:16.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.53
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6725.38
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.16e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.49
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:09.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.15
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.91
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:31.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:59.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907624
  j =  2                              :            46179
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908851
  j =  2                              :            45573
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:11.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.78e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.78e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.16
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.71
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:10.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17456.61
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:48.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.05
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:33.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:33.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.80
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.70
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.55
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.83
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.86
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5160.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.80
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.39
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.90
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.53
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.87
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.77
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.45
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3972.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.04
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.45
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999903335

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.10
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999934724

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.87
p-value of test                       :    0.9979

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:13.02

 All tests were passed




Server wird beendet - Lösche Semaphor 62849052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1520
p-value of test                       :  1.8e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334640
  j =  1                              :        599996960
  j =  2                              :             1520
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:46.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.79
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.68
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.99
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.91
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:34.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.29
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:21.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.81
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.54
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9911


-----------------------------------------------
CPU time used                    :  00:02:58.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908471
  j =  2                              :            45760
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908157
  j =  2                              :            45917
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 1.92e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.68e-4
p-value of test                       :  4.4e-3

Kolmogorov-Smirnov- statistic = D-    : 3.43e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.90
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.76
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.87
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:20.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.89
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.42
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.81
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.98
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.43
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.92
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.68
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.59
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.59
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.51
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.33
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.79
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.18
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.47
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.38
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.31
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.80
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  450.63
p-value of test                       :  6.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.92
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.31
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.50
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.38
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:29.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10143.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.86
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:14.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4088.27
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12136.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000065188

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.21
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000086698

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:24:24.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  5  CollisionOver, t = 3            1.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42893341.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:53.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.67
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    5.16
p-value of test                       :  2.4e-3

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.91
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.40
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:40.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.76
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.23
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.61
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.81
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  480.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1393.76
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:20.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.84
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4847.08
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:53.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907976
  j =  2                              :            46003
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45874
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869874
  j =  1                              :        399908253
  j =  2                              :            45872
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.80e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.38
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.73
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.77
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.71
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.72
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.92
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.66
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.91
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.16
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.01
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.86
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.69
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.20
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.93
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.99
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.52
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.15
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.95
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.02
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.87
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.18
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.49
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.81
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.58
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.06e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 9.99e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.47
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.67
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.09
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10131.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.9924

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5096.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5075.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4245.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11439.12
p-value of test                       :    0.9943

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.55
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999957809

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.65
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000058846

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.53
p-value of test                       :    0.06

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.65
p-value of test                       :    0.9960

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:48.75

 All tests were passed




Server wird beendet - Lösche Semaphor 44007453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:42.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:10.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.13
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1350.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6897.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:21.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.76
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.14
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46030
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870030
  j =  1                              :        399907943
  j =  2                              :            46024
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907900
  j =  2                              :            46047
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:32.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.16e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.30e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.40
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:51.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.66
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.22
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.36
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.18
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.90
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.38
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.91
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.70
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.37
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.19
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.69
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.50
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.24
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.14
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5088.69
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.45
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.23
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.48
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.94
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.71
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10058.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10141.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.04
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.55
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12154.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.94
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000051859

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.06
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000075781

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9985

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:03.98

 All tests were passed




Server wird beendet - Lösche Semaphor 45088797.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    2.67
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     269
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.10
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.61
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.86
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.89
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.26
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45680
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869680
  j =  1                              :        399908642
  j =  2                              :            45676
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907768
  j =  2                              :            46110
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:29.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.74e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.32
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17457.50
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.58
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.80
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.45
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.58
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.07
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.36
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.41
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.00
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.76
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.73
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.92
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.39
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.84
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.35
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.71
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.57
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.30e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.23e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.81
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9915.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.72
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4737.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4024.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.00
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999996671

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.43
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000005356

Normal statistic for number of bits   :   0.042
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:05.92

 All tests were passed




Server wird beendet - Lösche Semaphor 46104605.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4414
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.65
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.10
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.74
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.57
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.42
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.24
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.89
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:15.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.41
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.78
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908520
  j =  2                              :            45734
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46153
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870153
  j =  1                              :        399907701
  j =  2                              :            46139
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 4.49e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.73e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.25
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.29
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.22
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.09
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:42.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17398.34
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.65
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.94
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.47
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  590.14
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.93
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.90
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.58
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.76
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.01
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.40
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.76
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4868.99
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.42
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.50
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.13e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.74e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.9949

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10340.54
p-value of test                       :  8.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.27
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.19
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.01
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000006865

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.37
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000109147

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:08.29

 All tests were passed




Server wird beendet - Lösche Semaphor 47185949.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5315
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:45.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:22.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     337
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.71
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.02
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.46
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:33.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.48
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:03:19.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.19
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.13
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.10
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:29.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:56.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908140
  j =  2                              :            45924
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45903
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869903
  j =  1                              :        399908196
  j =  2                              :            45899
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:31.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    4.52
p-value of test                       :  5.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  6.1e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.49e-3
p-value of test                       :    0.9974

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.20e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:51.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.68
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.47
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   12.06
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.32
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.98
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.76
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.48
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.47
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.40
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.15
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.69
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.85
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.12
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.93
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.28
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  254.23
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.89
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.08
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.25
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.74
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.15
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10221.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:35.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12048.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.00
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000031033

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.89
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000010045

Normal statistic for number of bits   :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:15.27

 All tests were passed




Server wird beendet - Lösche Semaphor 48234525.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1470
p-value of test                       :  2.4e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334590
  j =  1                              :        599997060
  j =  2                              :             1470
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:16.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.12
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.22
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.51
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.83
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.78
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.96
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6799.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.79
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.25
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.67
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:37.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5027.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:09.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907974
  j =  2                              :            46001
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908529
  j =  2                              :            45728
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:34.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:21.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.57e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.87
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.98
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.38
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17122.18
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.95
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.73
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.07
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.94
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.77
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.35
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.67
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.80
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.19
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  321.21
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.73
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:03.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  153.44
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9912.74
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9786.24
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.77
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11424.14
p-value of test                       :    0.9958

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.67
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000010093

Normal statistic for number of bits   :   0.080
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.92
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000094039

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:13.20

 All tests were passed




Server wird beendet - Lösche Semaphor 49283101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997139
  j =  2                              :             1429
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:12.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    3.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.05
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.98
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.36
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.02
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7247.23
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.31
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.30
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.25
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:31.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46090
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870090
  j =  1                              :        399907825
  j =  2                              :            46080
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908678
  j =  2                              :            45655
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.50e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.89
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17647.24
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.75
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.48
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.88
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.55
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.74
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.32
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.68
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.79
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.25
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.86
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.35
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.17
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:20.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    2.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.65e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.64e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.77e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.64
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:01.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:02.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10037.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5019.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    5.94
p-value of test                       :  1.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5113.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11625.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.31
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999909938

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.49
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999979568

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:47.54

 All tests were passed




Server wird beendet - Lösche Semaphor 50298909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1463
p-value of test                       :  4.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334583
  j =  1                              :        599997074
  j =  2                              :             1463
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5544
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7143
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:16.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9951

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    5.04
p-value of test                       :  2.7e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   34.83
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.13
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5173.46
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908737
  j =  2                              :            45624
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46089
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870089
  j =  1                              :        399907822
  j =  2                              :            46089
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.29e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9992    *****

-----------------------------------------------
CPU time used                    :  00:00:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.10
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.71
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.74
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17370.25
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.23
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.45
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.02
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.79
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.44
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.56
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.55
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.49
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.61
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.62
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.72
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.87
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.04
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5177.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.33
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.61
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.17
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.83
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  156.35
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10202.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.08
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4315.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.83
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999872075

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.36
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999944666

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.66

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:04.42
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51314717.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7240
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:19.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:53.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    8.99
p-value of test                       :  4.2e-5    *****

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:19.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.42
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.94
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.75
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7279.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.49
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.03
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907955
  j =  2                              :            46018
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46130
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870130
  j =  1                              :        399907747
  j =  2                              :            46116
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:36.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.67e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.48
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.27
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.79
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.33
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.63
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.52
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.74
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.21
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.45
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.59
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.07
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.24
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.39
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.68
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.35
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.54
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.20
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.65
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.27
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.75
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  : -5.96e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.36
p-value of test                       :    0.9925


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.20
p-value of test                       :    0.99

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.54e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.56
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.20
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.45
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4907.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.63
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4234.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11467.23
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.93
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999921503

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.35
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000077464

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.93
p-value of test                       :    0.03

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.28
p-value of test                       :    0.99

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.19
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:12.38
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3          4.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52428829.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:07.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.79
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     255
p-value of test                       :    0.9957

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.93
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.77
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  489.57
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1394.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.33
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9956

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.07
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.68
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.81
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.81
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:32.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:58.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45912
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869912
  j =  1                              :        399908178
  j =  2                              :            45908
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908325
  j =  2                              :            45833
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.26e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.044
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.96
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.78
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.85
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.86
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.67
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.83
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.84
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.38
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.83
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.19
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.09
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.10
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.44
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.18
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.33
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.46
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.80
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.80
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.70
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.25
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.92
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.94
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.27
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.93e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.65
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:32.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4835.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.27
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4272.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11858.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.98
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999983498

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.41
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000087433

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:59.04

 All tests were passed




Server wird beendet - Lösche Semaphor 53477405.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:18.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.87
p-value of test                       :  3.7e-3

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:46.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:51.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.88
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7031.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.06
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.60
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.05
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908159
  j =  2                              :            45913
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907875
  j =  2                              :            46058
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.9922

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 6.46e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.96
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.092
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.41
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.57
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17115.31
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.31
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.70
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.22
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.70
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.85
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.54
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.83
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.71
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.37
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  251.76
p-value of test                       :  7.6e-3


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.16
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.95
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.50
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -2.07
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:18.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.84e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.28
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9852.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.29
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.13
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.94
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000066244

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.87
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999875021

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:06.27

 All tests were passed




Server wird beendet - Lösche Semaphor 54525981.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.06
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    5.48
p-value of test                       :  1.7e-3

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.38
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.78
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.09
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.30
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.36
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.80
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.54
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45575
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869575
  j =  1                              :        399908852
  j =  2                              :            45571
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908370
  j =  2                              :            45812
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.71
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.34
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.00
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:52.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.39
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.05
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.13
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.80
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.73
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.09
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.41
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.39
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.43
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.07
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.59
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.54
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.26
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.50
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5204.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.75
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.82
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.61
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.57
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.36
p-value of test                       :    0.91

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.56
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:21.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9905.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.44
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4980.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3851.89
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.04
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11549.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.08
p-value of test                       :  5.5e-3


-----------------------------------------------
Total number of bits:  7999828731

Normal statistic for number of bits   :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.35
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999948542

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.23

 All tests were passed




Server wird beendet - Lösche Semaphor 55541789.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:06.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:15.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.82
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1479.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.83
p-value of test                       :  1.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.49
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:21.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.13
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.80
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.74
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:02.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45806
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869806
  j =  1                              :        399908389
  j =  2                              :            45804
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908366
  j =  2                              :            45814
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:52.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.88
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17714.34
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.21
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.40
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.56
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.45
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.08
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.63
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.49
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.78
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.19
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5129.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.93
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.59
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.83
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.48
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.87
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.88e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.09
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:15.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:35.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.53
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4028.04
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11864.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.05
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999884390

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999948029

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:33.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:35.76

 All tests were passed




Server wird beendet - Lösche Semaphor 56590365.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:47.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.40
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.04
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6996.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:14.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.06
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4993.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:29.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:59.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908779
  j =  2                              :            45603
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45989
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869989
  j =  1                              :        399908029
  j =  2                              :            45975
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.03
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.57
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.43
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.94
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.67
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    4.39
p-value of test                       :  5.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.74
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17597.01
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.47
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.05
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.82
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.36
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.18
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.57
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.39
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.56
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.10
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.08
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.39
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.24
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.15
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.12
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.18
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.13
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.96
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.62
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.95
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :    1.03
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.11
p-value of test                       :    0.9999    *****

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.54e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.89
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.08
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.34
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:38.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.83
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:33.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999969743

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.59
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000016189

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:19.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :  -0.072
p-value of test                       :    0.53

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:14.38

 All tests were passed




Server wird beendet - Lösche Semaphor 57671709.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:13.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.58
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7065.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.34
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.36
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908196
  j =  2                              :            45893
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908069
  j =  2                              :            45958
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9971


-----------------------------------------------
CPU time used                    :  00:02:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.7e-3

Anderson-Darling statistic = A2       :    3.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:38.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.87
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.27
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17655.83
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.92
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.90
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.19
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.42
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.66
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.47
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.73
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.01
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.16
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.38
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.52
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.06
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.44
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.28
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.54
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.46
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.92
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.24
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10064.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:11.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.60
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4157.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12187.94
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000027337

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.01
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999948392

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.75

 All tests were passed




Server wird beendet - Lösche Semaphor 58720285.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    3.16
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     822
p-value of test                       :    0.9956

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:43.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.03
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.39
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  392.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1347.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.47
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.3e-4    *****

Anderson-Darling statistic = A2       :    4.87
p-value of test                       :  3.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.94
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:10.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.54
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.89
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5078.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908229
  j =  2                              :            45878
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46028
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870028
  j =  1                              :        399907946
  j =  2                              :            46024
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.07
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.63
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.10
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17357.89
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.34
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.19
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.50
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.27
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.73
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.53
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.13
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.60
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  549.32
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  169.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4962.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.93
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.57
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:20.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.56
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:20.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.72
p-value of test                       :  3.2e-3

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.68e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.70e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.62
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.46
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.13
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.11
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4205.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.45
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000096028

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.80
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000023101

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:12.88

 All tests were passed




Server wird beendet - Lösche Semaphor 59768861.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    5.39
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.16
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  500.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7324.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.76e-3
p-value of test                       :    0.9962

Kolmogorov-Smirnov- statistic = D-    :    0.68
p-value of test                       :  4.4e-3

Anderson-Darling statistic = A2       :    5.58
p-value of test                       :  1.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   60.02
p-value of test                       :  9.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.52e-4
p-value of test                       :    0.9991    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   86.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.66
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46108
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870108
  j =  1                              :        399907787
  j =  2                              :            46102
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45809
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869809
  j =  1                              :        399908389
  j =  2                              :            45795
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.96e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.73e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.01
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.92
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.44
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.25
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17448.48
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.93
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.22
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.65
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.09
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.27
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.98
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.34
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  561.73
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.12
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.76
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.48
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  440.59
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.13
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.87
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.53
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.06
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:20.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.53
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:20.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.85
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.018
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:10.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.72
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11785.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.66
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  7999895802

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.42
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000057625

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:37.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 38  Run, r = 0                      9.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60817437.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5416
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:45.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:11.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:12.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.62
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.68
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.25
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.98
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  356.72
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6904.12
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 3.17e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.03
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.98
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.99
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45607
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869607
  j =  1                              :        399908791
  j =  2                              :            45597
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908705
  j =  2                              :            45640
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.38e-5
p-value of test                       :    0.9924

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:43.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.84
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.49
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.77
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17120.20
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.51
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.34
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.74
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.66
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.93
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.55
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.72
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.82
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.46
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.74
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.41
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.98
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.92
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.58
p-value of test                       :  5.0e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.07
p-value of test                       :  2.8e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.84
p-value of test                       :    0.9977

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.47e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-4
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.57
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.34
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.97
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.094
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.93
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.26
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11722.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.19
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000017611

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.66
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000040975

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.020
p-value of test                       :    0.49

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:27.82

 All tests were passed




Server wird beendet - Lösche Semaphor 61866013.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5304
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:09.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     827
p-value of test                       :    0.9927

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:46.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.32
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.68
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.29
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1461.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6968.39
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.45
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.18
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5098.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:48.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907871
  j =  2                              :            46060
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908396
  j =  2                              :            45799
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:21.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.25e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.12
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.67
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.67
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.07
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.06
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.12
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:48.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.87
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:33.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.48
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.78
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:33.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.23
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.78
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.96
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.93
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.74
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.08
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.67
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.05
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.58
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.51
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.71
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.23

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.9956

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.55
p-value of test                       :  5.3e-3

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.89e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.24e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.61e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.72
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   24.99
p-value of test                       :  1.6e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.85
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9836.60
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.071
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.19
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4217.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11669.91
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.62
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999940667

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.97
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999958976

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.079
p-value of test                       :    0.53

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:02:41.22

 All tests were passed




Server wird beendet - Lösche Semaphor 62914589.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  5.8e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:49.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:00.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5514
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7460
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.66
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.55
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.85
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.28
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1372.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7149.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.56
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.00
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5067.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46236
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870236
  j =  1                              :        399907535
  j =  2                              :            46222
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908360
  j =  2                              :            45814
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:14.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:31.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.45e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.03e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.32
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.27
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.18
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.93
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:30.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17168.32
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.16
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.01
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.94
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.03
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.82
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.55
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.66
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.48
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.64
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.70
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5170.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.76
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.73
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.50
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.54
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.07
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.70
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.59
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:15.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.53
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:14.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    6.52
p-value of test                       :  6.0e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.72
p-value of test                       :  9.9e-5    *****

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.47e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 7.93e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.25e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.92
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.13
p-value of test                       :  7.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9617.86
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:20.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4703.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.65
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.59
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.12
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11970.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.82
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999999242

Normal statistic for number of bits   : -5.99e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.83
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000037189

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    2.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:17.09
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               5.8e-4
 83  LempelZiv, r = 15               9.9e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42926110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5578
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7102
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.90
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.12
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.45
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.89
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.31
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45682
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869682
  j =  1                              :        399908640
  j =  2                              :            45674
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46107
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870107
  j =  1                              :        399907787
  j =  2                              :            46105
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:19.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 9.56e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.83e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:51.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.21
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  151.94
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17269.72
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.48
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.32
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.95
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.09
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.95
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.36
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.98
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.42
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.09
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.43
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.65
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  306.80
p-value of test                       :    0.9985


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.23
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.87
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.19
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.81e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.24
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.18e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.26
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.60
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9823.20
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.85
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.75
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.00
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999917636

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.37
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000195016

Normal statistic for number of bits   :    1.54
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:15.35

 All tests were passed




Server wird beendet - Lösche Semaphor 43515934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7484
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:36.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7525
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    5.50
p-value of test                       :  1.7e-3

Stat. AD after spacings (mNP2-S)      :    2.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.73
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.42
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:11.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.37
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.18
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.27
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7160.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.58
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.29
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:40.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.09
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46122
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870122
  j =  1                              :        399907759
  j =  2                              :            46116
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908012
  j =  2                              :            45991
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:35.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:22.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.16e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.85
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.34
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.69
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.36
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17310.86
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.41
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.13
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.28
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.64
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.96
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.18
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.35
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.35
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.16
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.76
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.88
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4756.57
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.93
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.23
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.21
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.82
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.36
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.24
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :    1.24
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.75
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.13
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.84
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.16
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9838.87
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9865.62
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:30.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5045.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4116.82
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11740.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.27
p-value of test                       :    0.9944


-----------------------------------------------
Total number of bits:  8000097867

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.86
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999989579

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.086
p-value of test                       :    0.53

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:07.84

 All tests were passed




Server wird beendet - Lösche Semaphor 44204062.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:05.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:39.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7523
p-value of test                       :  8.7e-3


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.37
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.59
p-value of test                       :  1.7e-3

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:43.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.59
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.25
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.04
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.16
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.31
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:09.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7278.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.10
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.63
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:18.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.37
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.37
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.45
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908426
  j =  2                              :            45778
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907902
  j =  2                              :            46043
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:33.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.09e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.53e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.52
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.87
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.00
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-3
p-value of test                       :    0.9957

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.20
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17112.94
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   56.09
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.66
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.21
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.89
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.57
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.41
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.06
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.77
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.53
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.28
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.07
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.37
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.70
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.77
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.03
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.36
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.71e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.74
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.99
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.75
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:08.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:30.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.67
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4333.85
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11659.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.09
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999989027

Normal statistic for number of bits   :  -0.087
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.43
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000152566

Normal statistic for number of bits   :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:14.07

 All tests were passed




Server wird beendet - Lösche Semaphor 45482014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:41.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:55.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:04.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:03:57.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.57
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.02
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.29
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.68
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.68
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6798.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.54
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4889.52
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46027
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870027
  j =  1                              :        399907948
  j =  2                              :            46023
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908075
  j =  2                              :            45958
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:31.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:44.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.97
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.55
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   70.69
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.55
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.93
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   51.75
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.95
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.21
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    4.83
p-value of test                       :    0.9982


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.06
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.26
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.23
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.27
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.31
p-value of test                       :  8.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.64
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.07
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.22
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.09
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.11
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.53
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.50
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.89
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.08
p-value of test                       :    0.9950


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.67
p-value of test                       :    0.05

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.08e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.62e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.13
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.62
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.98
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:19.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.09
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999954227

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000000169

Normal statistic for number of bits   : 1.34e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:57.69

 All tests were passed




Server wird beendet - Lösche Semaphor 46694430.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5485
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7127
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:58.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:01.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    5.05
p-value of test                       :  2.7e-3

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:49.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.74
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.37
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.78
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.93
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6812.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.88
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   96.21
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.21
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46209
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870209
  j =  1                              :        399907585
  j =  2                              :            46203
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:20.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.98e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.15
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.37
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17552.34
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.23
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.20
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.34
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   61.79
p-value of test                       :  4.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.18
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.10
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.92
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.08
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.03
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.91
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.66
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.16
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.69
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.33
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.15
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.54
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.19
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.64
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.12
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.30
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.15
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.36
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9828.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.14
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11655.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11998.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.27
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000097186

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.81
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000046465

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.61e-3
p-value of test                       :    0.9919

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:12.79

 All tests were passed




Server wird beendet - Lösche Semaphor 47677470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.32
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.97
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.66
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.27
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.87
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.49
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5024.01
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908205
  j =  2                              :            45893
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908331
  j =  2                              :            45830
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  1.2e-4    *****

Anderson-Darling statistic = A2       :    9.47
p-value of test                       :  2.5e-5    *****


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 3.39e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.01e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.82
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.43
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.32
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.24e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17303.97
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.13
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.62
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.85
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.32
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.98
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  560.12
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.37
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.76
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.38
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.77
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.19
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  307.99
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.21
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.55
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.20
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.03
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.86
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.94
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.33
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:25.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.35e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.03
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.64
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.30
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.51
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.46
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.81
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000010813

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.46
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000040627

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   0.045
p-value of test                       :    0.48

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:21.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                2.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48660510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5344
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7091
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:02:41.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4255
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7145
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.15
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.75
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.16
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1551.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.73e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:07.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.12
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.43
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46360
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870360
  j =  1                              :        399907282
  j =  2                              :            46356
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.39e-3
p-value of test                       :    0.9950

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.19e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.44e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.68
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.50
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.13
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.34
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.17
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.86
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.69
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.92
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   50.65
p-value of test                       :  3.3e-5    *****


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.02
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.05
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.69
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.58
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.79
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.21
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.85
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.00
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.92
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4862.26
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.86
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.30
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.11
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.27
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.44
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10057.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.13
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:32.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11739.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.53
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000076753

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.14
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999917858

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:39.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 74  RandomWalk1 C (L=50, r=0)       3.3e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49610782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4192
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7128
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.60
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    2.54
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.15
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.21
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.14
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.77
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.95
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.87
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.74
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908494
  j =  2                              :            45747
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908178
  j =  2                              :            45905
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.29e-3
p-value of test                       :    0.9935

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:58.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.96
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.10
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.16
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.67
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.61
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.65
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.51
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.27
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.08
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.58
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.22
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.19
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.29
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.54
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.45e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.36
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:40.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.76
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.75
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.99
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999945218

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.96
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000054631

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:42.01

 All tests were passed




Server wird beendet - Lösche Semaphor 50528286.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:11.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:13.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.54
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:47.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.51
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.50
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.59
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.89
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6970.44
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.95
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.80
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.54
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:13.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45824
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869824
  j =  1                              :        399908354
  j =  2                              :            45820
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45536
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869536
  j =  1                              :        399908934
  j =  2                              :            45524
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:09.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.3e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 2.33e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 5.68e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.01
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.68
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17164.49
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.83
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.63
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.65
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.34
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.38
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.42
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.46
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.81
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.08
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.83
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.01
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.07
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  416.17
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.06
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:27.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.71e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:40.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.14
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.34
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:28.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11765.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:33.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.23
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999873497

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.81
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999930221

Normal statistic for number of bits   :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:22.22

 All tests were passed




Server wird beendet - Lösche Semaphor 51773470.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:54.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     970
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    4.12
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    3.96
p-value of test                       :  9.1e-3

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:48.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.73
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.71
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.72
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.68
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:01.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7008.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.54
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4985.62
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:57.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908013
  j =  2                              :            45986
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907737
  j =  2                              :            46118
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.45e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:20.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:40.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17573.80
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.67
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.26
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.30
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.88
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.57
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.22
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.04
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.98
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.92
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.53
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.38
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.62
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.20
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.91
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.44
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.63
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4891.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.17
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.71
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.69
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 5.83e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.20
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.42
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.70
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.50
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.70
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999989213

Normal statistic for number of bits   :  -0.085
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.39
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999782768

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.95

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    2.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:14.39

 All tests were passed




Server wird beendet - Lösche Semaphor 53248030.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5431
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:03.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.58
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.57
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.22
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.26
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.86
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4867.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:03:05.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908209
  j =  2                              :            45894
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45771
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869771
  j =  1                              :        399908461
  j =  2                              :            45765
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:17.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.11e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.35
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.64
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.11
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.03
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  166.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:42.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17531.40
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.00
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.87
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.66
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.38
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.99
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.73
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.75
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.26
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.16
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.46
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.71
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.36
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.56
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.17
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.37e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.94
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  160.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.87
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.72e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9630.34
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10023.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:18.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.64
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.67
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11641.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.56
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000110446

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.51
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999993770

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:00.51

 All tests were passed




Server wird beendet - Lösche Semaphor 54165534.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:42.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.19
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.60
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.21
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.89
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.24
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.78
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1409.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6913.54
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:19.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.27
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.88
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908779
  j =  2                              :            45603
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46412
p-value of test                       :  6.6e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870412
  j =  1                              :        399907180
  j =  2                              :            46404
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:33.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:11.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.42e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.35
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.85
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.13
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.38
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.15
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17628.93
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.19
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.49
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.36
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.08
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.62
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.90
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.18
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.35
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.71
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.04
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4721.80
p-value of test                       :    0.9977


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.25
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.68
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.52
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.21
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.33
p-value of test                       :    0.99

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 4.73e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.59
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.11
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10044.53
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:04:26.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.57
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4901.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:01.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4044.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.91
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.33
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.77
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000015574

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.18
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000033919

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:21.13

 All tests were passed




Server wird beendet - Lösche Semaphor 55214110.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:14.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:15.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.54
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.11
p-value of test                       : 1 -  5.8e-5    *****

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:49.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.45
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.58
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7105.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:11.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   83.78
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.23
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:00.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908216
  j =  2                              :            45889
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46031
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870031
  j =  1                              :        399907942
  j =  2                              :            46023
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 5.79e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.31e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.46e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.31
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.58
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.69
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.18
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.74
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.81
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.33
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.28
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.62
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.69
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  588.81
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.21
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.73
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  252.57
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:00:36.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.10
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.42
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.32
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.50
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.34e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.67
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:32.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.92
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.17
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10079.09
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.06
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.67
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11824.54
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.69
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000047125

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.19
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999963929

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:48.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP2, t = 3         1 -  5.8e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56360990.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9901


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:48.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4208
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.69
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.30
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  461.48
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1533.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.56
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.53
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.48
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.39
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5058.01
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:19.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908381
  j =  2                              :            45805
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45718
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869718
  j =  1                              :        399908567
  j =  2                              :            45712
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.37e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 2.04e-4
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:26.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.25
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.9928

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.62
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.033
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.12
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.11
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.66
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.84
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.40
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.47
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.04
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.12
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.06
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.52
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.77
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.84
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.17
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.90
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.55
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.38
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.89
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.54
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:27.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 4.41e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.76
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.72
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9801.92
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4728.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.78
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4137.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.85
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000030175

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.85
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000022717

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:08.46

 All tests were passed




Server wird beendet - Lösche Semaphor 57442334.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9983


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5469
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7509
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:07.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     848
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    4.52
p-value of test                       :  4.9e-3

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.41
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.29
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.73
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.93
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4938.20
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908075
  j =  2                              :            45955
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908162
  j =  2                              :            45913
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:29.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.08e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.47e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.43e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.91
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.33
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.11
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.19
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17397.32
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.45
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.06
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.53
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.29
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.46
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.81
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.95
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.92
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.63
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.83
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.81
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.84
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.55
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4809.24
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  444.04
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.84
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.28
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.33
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.31
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.82
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.76
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9688.34
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:13.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5094.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4276.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11859.44
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11799.37
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.69
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000085741

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.72
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000032050

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:17.70

 All tests were passed




Server wird beendet - Lösche Semaphor 58490910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7197
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:10.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     852
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:45.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.94
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.69
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1306.58
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.07
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.11
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.10
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.09
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46032
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870032
  j =  1                              :        399907937
  j =  2                              :            46030
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908143
  j =  2                              :            45924
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.15e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.93e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 6.76e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:45.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.86
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.17
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.21
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.05
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.39
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.26
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.35
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.19
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.87
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.77
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.17
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.43
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.35
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.57
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:09.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9717.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10115.03
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.80
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.15
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.27
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999993947

Normal statistic for number of bits   :  -0.048
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000003175

Normal statistic for number of bits   :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         : -9.22e-3
p-value of test                       :    0.50

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:51.73

 All tests were passed




Server wird beendet - Lösche Semaphor 59506718.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4471
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:05.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.43
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.71
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.31
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.07
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.97
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.65
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.80
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.18
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:02.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908384
  j =  2                              :            45802
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908479
  j =  2                              :            45753
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.51e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.18
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   49.62
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.59
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:41.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17193.91
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.18
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.03
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.77
p-value of test                       :    0.9905


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.89
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.43
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.59
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  575.68
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.84
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.88
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.51
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.02
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.63
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.29
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.89
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.79
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.80
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.44
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.17
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.86
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 6.19e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.61
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.13
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  172.94
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10300.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.69
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11615.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.71
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000126340

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.47
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999997685

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:11.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.40

 All tests were passed




Server wird beendet - Lösche Semaphor 60489758.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5483
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7533
p-value of test                       :  6.3e-3


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    2.17
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:43.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.04
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.63
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.92
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.25
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4806.57
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:03.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908201
  j =  2                              :            45892
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:19.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.98
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.79
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.73
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.10
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9976

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.23
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.84
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17274.73
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.32
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.82
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.87
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.17
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.06
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.34
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.22
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.77
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.65
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.88
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.44
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.86
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.40
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.25e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.93e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.46
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.39
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.15
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.64
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4250.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.62
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000075034

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.62
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999957026

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.04

 All tests were passed




Server wird beendet - Lösche Semaphor 61472798.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5507
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:11.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     962
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.34
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     257
p-value of test                       :    0.9939

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:17.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.84
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.86
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.85
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.66
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7133.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:20.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.53
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907761
  j =  2                              :            46118
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908668
  j =  2                              :            45666
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :  1.0e-3

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.6e-3


-----------------------------------------------
CPU time used                    :  00:02:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.87e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.99e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.37e-5
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.94
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.68
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.34
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.77
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.73
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.95
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.69
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.06
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.05
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.68
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.45
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.66
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.76
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.30
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.19
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.30
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.95
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.45
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.77
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.96
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.71
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:34.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.12
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.26
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  235.83
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.45
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.96
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.32e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.64e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:42.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.66
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.93
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.91
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.84
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4207.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.74
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000121711

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.17
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000025900

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:01.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    5.01
p-value of test                       :  3.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.74
p-value of test                       :    0.9969

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:49.70

 All tests were passed




Server wird beendet - Lösche Semaphor 62488606.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5573
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:06.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7111.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.74
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.56
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.84
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.34
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:15.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908162
  j =  2                              :            45910
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45585
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869585
  j =  1                              :        399908836
  j =  2                              :            45573
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 6.01e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.84
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.90
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.94
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.48
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.41
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.94
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17154.85
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.16
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.38
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.93
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.81
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.79
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.69
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.32
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.75
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.57
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.01
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  429.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.20
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.45
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.46
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.49
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.48
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.31
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.80
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.86
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:15.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :  -0.049
p-value of test                       :    0.52

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 9.49e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.88
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9784.51
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4141.73
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.48
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12002.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.81
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000056377

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.30
p-value of test                       :  4.2e-3


-----------------------------------------------
Total number of bits:  8000063256

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:00.59

 All tests were passed




Server wird beendet - Lösche Semaphor 42958879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:42.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:44.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    4.47
p-value of test                       :  5.2e-3

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.12
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    3.11
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:35.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.12
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.17
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1523.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7216.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.07
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45923
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869923
  j =  1                              :        399908160
  j =  2                              :            45911
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908300
  j =  2                              :            45844
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:34.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.09
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17542.20
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:54.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.33
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.99
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.47
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.87
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.90
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.00
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.29
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.26
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.16
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.99
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.05
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.24
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.20
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.66
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.86
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.41
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.67
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.37
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.19
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.18
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.022
p-value of test                       :    0.51

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.60e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.33e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.60
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:10.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.57
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:22.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4974.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11974.76
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11867.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.67
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000118540

Normal statistic for number of bits   :    0.94
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.91
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999974738

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:06.05

 All tests were passed




Server wird beendet - Lösche Semaphor 43319327.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:44.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9968

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.07
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.09
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.21
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6967.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.54
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.76
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908875
  j =  2                              :            45555
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45797
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869797
  j =  1                              :        399908410
  j =  2                              :            45789
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.02e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.08e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   97.68
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.51
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.36
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:39.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17699.90
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.01
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.96
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.68
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.29
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.14
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.84
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.62
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.72
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.27
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.20
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.50
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.52
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.11
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.57
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.21
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.22
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  452.25
p-value of test                       :  5.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.37
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.57
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.83
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.70
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10162.51
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:21.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4301.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.54
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999996347

Normal statistic for number of bits   :  -0.029
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999886658

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :  -0.031
p-value of test                       :    0.51

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:56.40

 All tests were passed




Server wird beendet - Lösche Semaphor 44400671.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:36.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4490
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7448
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.67
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    2.19
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.71
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:04.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.01
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.51
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.13
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:09.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.28
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.52
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.04
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908448
  j =  2                              :            45770
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45740
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869740
  j =  1                              :        399908524
  j =  2                              :            45732
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.62e-3
p-value of test                       :    0.9983

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.36
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.55
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.35
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.62
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.52
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.18
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.86
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.75
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.14
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.95
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.00
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  600.53
p-value of test                       :  1.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.42
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.50
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.45
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.25
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.27
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  153.92
p-value of test                       :    0.9933


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.05
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.26
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4618.16
p-value of test                       : 1 -  4.5e-5    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.02
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.58
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -2.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.66e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.81
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.01
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.23
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.088
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.36
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.88
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000092215

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.06
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000132562

Normal statistic for number of bits   :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.059
p-value of test                       :    0.52

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:46.60
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 J (L=10000, r=15)  1 -  4.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45187103.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5330
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:53.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7553
p-value of test                       :  3.2e-3


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:07.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:11.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:40.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.72
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.21
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1384.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6889.60
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:00.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.99
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.56
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.52
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:56.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908259
  j =  2                              :            45866
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908660
  j =  2                              :            45664
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:10.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:25.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.34
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.17
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.83
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.32
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.76
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.80
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.26
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.20
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.58
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.63
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.87
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.76
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.21
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.87
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.60
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.33
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5198.76
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.67
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.66
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.79
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.13
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.88
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.83

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 8.92e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.25
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.25
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.69
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.74
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9872.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.013
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:35.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12026.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:34.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.36
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999941846

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.66
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000004789

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:04.62

 All tests were passed




Server wird beendet - Lösche Semaphor 46235679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4376
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:04.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     847
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.34
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.33
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.72
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.95
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.99
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.60
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.20
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:06.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907603
  j =  2                              :            46194
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908181
  j =  2                              :            45908
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.22e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.42e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.39
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  163.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17193.68
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.60
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.76
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.99
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.04
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.72
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.44
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.89
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.77
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.07
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.56
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.51
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  316.35
p-value of test                       :    0.9950


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.21
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.50
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.30
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.93
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -1.56
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -1.37
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.04
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.52
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9875.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.36
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 8.99e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4671.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11854.70
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.28
p-value of test                       :    0.76


-----------------------------------------------
Total number of bits:  7999853937

Normal statistic for number of bits   :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.58
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000159025

Normal statistic for number of bits   :    1.26
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:19.54

 All tests were passed




Server wird beendet - Lösche Semaphor 47611935.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:57.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:11.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    4.24
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.28
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.75
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.67
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1543.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7229.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.36
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.48
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:56.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908188
  j =  2                              :            45903
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45656
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869656
  j =  1                              :        399908688
  j =  2                              :            45656
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:31.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.82
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.53e-4
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 3.27e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:25.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:25.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.50
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.62
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.3e-3

Anderson-Darling statistic = A2       :    3.56
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   59.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17255.70
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.51
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.36
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.69
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.75
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.93
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.57
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.45
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  449.42
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5166.84
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  475.71
p-value of test                       :  4.7e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.79
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.72
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.84
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.86
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.47
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.05
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.17e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.57
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.17
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:25.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.26
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:04:26.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.39
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:58.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.53
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11568.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.41
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999951338

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.34
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000049939

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:26.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 R (L=10000, r=0)    4.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48594975.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7476
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.68
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.54
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.63
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.04
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.11
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.72
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.14
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.14
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45663
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869663
  j =  1                              :        399908678
  j =  2                              :            45655
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45484
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869484
  j =  1                              :        399909034
  j =  2                              :            45480
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.54
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.02
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.32
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17475.38
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.45
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.83
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.73
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.11
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.92
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.97
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.89
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.89
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.67
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.69
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.62
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.42
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  312.76
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.35
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.92
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.31
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.00
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.68
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.37
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.72
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.03
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.32
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.34
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:22.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5050.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.33
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999972380

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.28
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999933734

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.67
p-value of test                       :    0.9963

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.030
p-value of test                       :    0.49

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.29

 All tests were passed




Server wird beendet - Lösche Semaphor 50069535.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1461
p-value of test                       :  4.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334581
  j =  1                              :        599997078
  j =  2                              :             1461
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4182
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7436
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:06.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.18
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.65
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.97
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.27
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.58
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7168.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.37
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.06
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4958.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45962
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869962
  j =  1                              :        399908079
  j =  2                              :            45956
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908609
  j =  2                              :            45688
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.44e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.70e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.38e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:45.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.09
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.01
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.35
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.98
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.39
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.76
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.29
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.56
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.62
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.68
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.50
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.81
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.41
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.66
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.75
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.98
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.66
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.34
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.23
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.78
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:26.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 2.90e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.92
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10258.71
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.06
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:16.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.09
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11952.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.78
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999983939

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.46
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000000016

Normal statistic for number of bits   : 1.26e-4
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.078
p-value of test                       :    0.53

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:10.59

 All tests were passed




Server wird beendet - Lösche Semaphor 51150879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:51.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1236
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334356
  j =  1                              :        599997528
  j =  2                              :             1236
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5394
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.70
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:16.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.13
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7120.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.14
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.07
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.51
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:32.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:35.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46172
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870172
  j =  1                              :        399907660
  j =  2                              :            46164
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45776
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869776
  j =  1                              :        399908449
  j =  2                              :            45774
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:20.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.19e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.73
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.25
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.50
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.97
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.89
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.64
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.42
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.48
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.81
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.12
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4841.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.83
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.11
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.30
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.15
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.76
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.90
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.65
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.48
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.76
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9945

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.81
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9676.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.92
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12164.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.31
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000048286

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.08
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000114988

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:05.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52101151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:52.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5356
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.27
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.14
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:01.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.07
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.31
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45920
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869920
  j =  1                              :        399908163
  j =  2                              :            45914
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908177
  j =  2                              :            45907
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 7.25e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.044
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.93
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.65
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.9969

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   18.55
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.24
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17491.49
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:54.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.42
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.74
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.45
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.17
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.52
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.64
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.87
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.81
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.53
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.64
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.62
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.82
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.77
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.20
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.36
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.18
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.14
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:27.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.34e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.95
p-value of test                       :    0.03

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 2.27e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.04
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.63
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.39
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.00
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4896.80
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.94
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12057.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.81
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.71
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000061423

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.64
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000051688

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :  -0.018
p-value of test                       :    0.51

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:37.25

 All tests were passed




Server wird beendet - Lösche Semaphor 53215263.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4142
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:42.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.37
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    2.59
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.11
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.85
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.26
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6966.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.11
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.71
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907516
  j =  2                              :            46239
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 1.99e+6
p-value of test                       :    0.9971


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.94e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   99.62
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17538.64
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.56
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.76
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.89
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.73
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.82
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.83
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.06
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.09
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.35
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  321.00
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4930.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.19
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.54
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.81
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.62
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.06

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.44e-3
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.89
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.73
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:20.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.62
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4327.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.96
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999968849

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.05
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000045604

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:56.26

 All tests were passed




Server wird beendet - Lösche Semaphor 54132767.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:55.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:41.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:59.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.77
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  276.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6992.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.63
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.34
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:56.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908670
  j =  2                              :            45656
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908054
  j =  2                              :            45970
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.64e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.91
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.96
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.21
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.89
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.02
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.12
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.72
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.14
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.83
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.49
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.87
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.92
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.69
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.24
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.74
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.74
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.05
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.64
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.61
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.22
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.55
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.65
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.77
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 9.59e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.14
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.33
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9799.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:18.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4120.39
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.82
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12049.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999884906

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.58
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000176215

Normal statistic for number of bits   :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:05.26

 All tests were passed




Server wird beendet - Lösche Semaphor 55181343.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:08.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.89
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    4.27
p-value of test                       :  6.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     533
p-value of test                       :    0.9971

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.04
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.86
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.76
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.34
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.03
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.91
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.31
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46064
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870064
  j =  1                              :        399907877
  j =  2                              :            46054
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908408
  j =  2                              :            45787
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:31.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:24.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.44e-5
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.70
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.74
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.48
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.63
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.99
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.88
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.59
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.74
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.61
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.37
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5174.73
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.52
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.82
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.95
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:25.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.44e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.47e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.61
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:20.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:20.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:38.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.85
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.43
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.32
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.62
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.10
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999861416

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.43
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999920621

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:35.79

 All tests were passed




Server wird beendet - Lösche Semaphor 56197151.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:43.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:07.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.60
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9988

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.61
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.85
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.53
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7143.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.47
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.67
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.77
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5047.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45728
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869728
  j =  1                              :        399908547
  j =  2                              :            45722
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45393
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869393
  j =  1                              :        399909218
  j =  2                              :            45385
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:19.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.16e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.10e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.98e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.24
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.26
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:49.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.63
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.58
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.50
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.22
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.65
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.70
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.21
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.08
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.81
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.20
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.59
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.25
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  196.20
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.17
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.25
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.23
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.87
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5268.64
p-value of test                       :  4.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.72
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.73
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.24
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.89
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.63
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.13
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:26.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.45
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.55
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.37
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.32
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10244.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.21
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12207.42
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.14
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000079807

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.42
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999970034

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:10.54

 All tests were passed




Server wird beendet - Lösche Semaphor 57409567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:44.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4243
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:00.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:10.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    3.16
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6929.95
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:19.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.41
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:47.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.28
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.11
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46036
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870036
  j =  1                              :        399907928
  j =  2                              :            46036
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45885
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869885
  j =  1                              :        399908233
  j =  2                              :            45879
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:32.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:50.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.00
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.59e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.60
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   53.03
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.42
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.11
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.84
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.43
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.91
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.20
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.88
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.29
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.82
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.68
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.90
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.41
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.41
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.98
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.40
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.05
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.79
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.92
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.31
p-value of test                       :    0.9929


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.087
p-value of test                       :    0.47

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.81e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.99
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:21.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.07
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11930.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12184.82
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.54
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999887351

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.60
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999945212

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:45.73

 All tests were passed




Server wird beendet - Lösche Semaphor 58458143.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:07.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9955

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    4.15
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.02
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:15.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.61
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.30
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.52
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:09.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4858.80
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:59.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907456
  j =  2                              :            46266
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908490
  j =  2                              :            45749
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.29
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17411.90
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:53.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.83
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.68
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.95
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.31
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.81
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.24
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.69
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.28
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.26
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.27
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.03
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.80
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.23
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  303.00
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.85
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.47
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.84
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.97
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.11
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -2.87
p-value of test                       :    0.9980



-----------------------------------------------
CPU time used                    :  00:02:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 8.54e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.69
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.59
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.14
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9846.97
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.81
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.54
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.87
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4056.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.95
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.81
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000024835

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.84
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000026920

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:23.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 M (L=10000, r=0)    0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59539487.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1226
p-value of test                       : 1 -  7.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334346
  j =  1                              :        599997548
  j =  2                              :             1226
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5398
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4421
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.24
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:43.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.35
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   38.47
p-value of test                       :  3.4e-3

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.95
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.04
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.11
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.13
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.22
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.52
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.77
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.73
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:00.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46136
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870136
  j =  1                              :        399907732
  j =  2                              :            46128
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45503
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869503
  j =  1                              :        399909002
  j =  2                              :            45487
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 8.64e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:50.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.27
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.18
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17104.24
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.69
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.73
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.97
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.36
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.55
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  189.80
p-value of test                       :  8.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.07
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.52
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.15
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.27
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.50
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.23
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.13
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.22
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.06
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.94
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.80
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.31
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   -1.29
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.40e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.89
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.63
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.20
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10269.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:12.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.33
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.73
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.56
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.03
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11673.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11851.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.55
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000060541

Normal statistic for number of bits   :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.85
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000066325

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.07
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:40.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 10  CollisionOver, t = 14          1 -  7.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60522527.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5479
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:14.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    2.33
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     842
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.57
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    4.71
p-value of test                       :  4.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:17.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.80
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.98
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.25
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1410.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7254.53
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.99
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.44
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.78
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:01.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908252
  j =  2                              :            45868
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907953
  j =  2                              :            46016
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.32e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.01e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.04
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.70e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.57
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.73
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.32
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.73
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.69
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.58
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.05
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.22
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.71
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.95
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.28
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.26
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.98
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.57
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 8.39e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.97
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:06.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.86
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4708.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.71
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:59.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11735.88
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11755.04
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999969668

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.03
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999940409

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:14.04

 All tests were passed




Server wird beendet - Lösche Semaphor 61538335.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7550
p-value of test                       :  3.6e-3


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.56
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.15
p-value of test                       :    0.9987

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:45.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.61
p-value of test                       :    0.9936

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.85
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.96
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  396.54
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1466.92
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.80
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.16
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   84.31
p-value of test                       :    0.9932


-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.47
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46219
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870219
  j =  1                              :        399907572
  j =  2                              :            46199
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.28e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.65
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.41
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.98
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.73
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.07
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.60
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.91
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.28
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.70
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.14
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.43
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.84
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.05
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.41
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5178.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.03
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4977.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.29
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:33.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.44
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.72
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.47e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.21e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.34
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:59.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9855.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:22.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.95
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000044746

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999860234

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:02:57.23

 All tests were passed




Server wird beendet - Lösche Semaphor 62619679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:49.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:03.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:57.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     846
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:37.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.15
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.79
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6973.49
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.04
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.32
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.22
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907804
  j =  2                              :            46095
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46274
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870274
  j =  1                              :        399907455
  j =  2                              :            46268
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:31.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.40e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.67
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.85
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.51
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.74
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:41.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17321.47
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.76
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.32
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:40.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.43
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.93
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.34
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.26
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.58
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:48.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.52
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.84
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.72
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.16
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.83
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.05
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.90
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.15
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.65
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:34.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.89
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:14.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.14
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:11.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:48.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.43
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.08
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.40
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.36
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.52
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.46
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999958181

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.66
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  7999988727

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.21

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.9931

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:11.62

 All tests were passed




Server wird beendet - Lösche Semaphor 42991648.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:10.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.58
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     183
p-value of test                       :  5.0e-3

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:31.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.59
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.72
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.99
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7144.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.38
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5036.22
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46120
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870120
  j =  1                              :        399907762
  j =  2                              :            46116
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908332
  j =  2                              :            45828
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
p-value of test                       :    0.9967

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:01.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.60
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.80
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.87
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.10
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.27
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.26
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.03
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17244.69
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.74
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.45
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.30
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.91
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.60
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:39.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.41
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.17
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.41
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.03
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.64
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  447.21
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.96
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.25
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.66
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.67
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.24
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.56
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:37.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.72
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:18.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.40
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.81
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:10.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:22.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5077.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.9939

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5154.23
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3926.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.35
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11684.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.15
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000061426

Normal statistic for number of bits   :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.33
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999925628

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.029
p-value of test                       :    0.51

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.61
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:48.77

 All tests were passed




Server wird beendet - Lösche Semaphor 43548704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5412
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:47.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7118
p-value of test                       :    0.9905


-----------------------------------------------
CPU time used                    :  00:04:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.72
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.38
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.32
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.25
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.54
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.80
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1553.58
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6984.76
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.53
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.32
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:17.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5015.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:40.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907839
  j =  2                              :            46076
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45850
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869850
  j =  1                              :        399908306
  j =  2                              :            45838
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.11
p-value of test                       :  2.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.9977


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:11.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.29e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.70e-5
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:25.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.13
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:01.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.63
p-value of test                       :    0.9915

-----------------------------------------------
CPU time used                    :  00:00:52.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.99
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.29
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.83
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17201.57
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:54.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.47
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.58
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.77
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.75
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.66
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.22
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.81
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.72
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.81
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.05
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  462.35
p-value of test                       :  3.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.60
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.88
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  243.07
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.20
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.18
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.00
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.91
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.16
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    2.79
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.39e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.07
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:36.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4810.20
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:58.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.05
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.48
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11474.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.08
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  8000197374

Normal statistic for number of bits   :    1.56
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.70
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000031033

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.048
p-value of test                       :    0.52

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:57.84

 All tests were passed




Server wird beendet - Lösche Semaphor 44367904.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:39.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:38.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:55.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4351
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:05.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     579
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.04
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.15
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:40.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  393.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1325.06
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9950

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.78
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   17.26
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.02
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.63
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:59.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908621
  j =  2                              :            45682
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908386
  j =  2                              :            45798
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.68e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.36e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.77e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.20
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.60
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17669.19
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.76
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.94
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.56
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.43
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.29
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.96
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.42
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.72
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.08
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.65
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.01
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.18
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.31
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.28
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.06
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.89
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.43
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.75

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.88e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.06
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.81
p-value of test                       :    0.9992    *****

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.42
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.81
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:09.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.71
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:22.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4648.23
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:55.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11664.52
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12024.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.04
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999966365

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.69
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999978383

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.97
p-value of test                       :    0.98

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:54.14
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 87  LongestHeadRun, r = 27          0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45908000.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5362
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:38.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4174
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:04.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    3.60
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.83
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.63
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.96
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1509.51
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.83
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  156.04
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.67
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:06.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45517
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869517
  j =  1                              :        399908969
  j =  2                              :            45511
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45573
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869573
  j =  1                              :        399908855
  j =  2                              :            45571
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.43e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 2.09e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.00
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.15
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.29
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.18
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17163.89
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.32
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.79
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.17
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.90
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.45
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.91
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.13
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.71
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.36
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.81
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.40
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.69
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.07
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.27
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.99
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.52
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.36e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.62
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.15
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9906

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.43
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.074
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:20.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.01
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.02
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11781.78
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.46
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.83
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999878477

Normal statistic for number of bits   :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.57
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000193972

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.80

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:35.46

 All tests were passed




Server wird beendet - Lösche Semaphor 46891040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:58.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1248
p-value of test                       :    0.9993    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334368
  j =  1                              :        599997504
  j =  2                              :             1248
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:52.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:39.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:05.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9932


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.79
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:15.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.12
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.46
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.64
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1380.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.42
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:17.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.62
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.91
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.51
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45605
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869605
  j =  1                              :        399908793
  j =  2                              :            45599
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45812
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869812
  j =  1                              :        399908383
  j =  2                              :            45798
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.73e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.68e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.89e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.80
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17651.53
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.59
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.67
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.53
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.30
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.02
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.08
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.50
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.94
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.46
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.14
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.51
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4963.42
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.67
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.42
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.54
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  319.04
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.98
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.14
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-3
p-value of test                       :    0.9988

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.99e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.07
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.26
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10087.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.031
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5059.23
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.18
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.48
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000080158

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.14
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000053854

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    2.35
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.81
p-value of test                       :    0.21

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:04.05
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9993 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47775776.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:41.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997457
  j =  2                              :             1270
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:09.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:15.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     829
p-value of test                       :    0.9913

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.67
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.19
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.07
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.74
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7166.30
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.89
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.15
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.06
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908037
  j =  2                              :            45974
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908174
  j =  2                              :            45907
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:20.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:08.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 6.57e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.061
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.93
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.72
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.83
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.66
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17146.31
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.98
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.76
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.34
p-value of test                       :    0.9906


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.01
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.52
p-value of test                       :    0.9900


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.53
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.02
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.60
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.71
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.43
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.94
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.96
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.23
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.05
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -3.01
p-value of test                       :    0.9987



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.13e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.48
p-value of test                       :    0.9931

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.36
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9704.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.09
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:37.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.71
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.73
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.56
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:33.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.11
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.98
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999905357

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.29
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000070429

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:24.57

 All tests were passed




Server wird beendet - Lösche Semaphor 48824352.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5363
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:54.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7539
p-value of test                       :  5.2e-3


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.20
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.07
p-value of test                       :  8.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.04
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.69
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7009.66
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.41
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.04
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.01
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45568
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869568
  j =  1                              :        399908868
  j =  2                              :            45560
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45701
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869701
  j =  1                              :        399908600
  j =  2                              :            45697
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:19.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.93e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.72
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.80
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.41
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.41
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.97
p-value of test                       :  9.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.49
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.23
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  172.12
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.72
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:54.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.14
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.32
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.57
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.03
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.39
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.64
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.16
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.37
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.86
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.39
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.83
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.43
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.83
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :    1.77
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.16e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.29e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.73
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.09
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:16.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4823.77
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11773.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.88
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999985049

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000057904

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:31.69

 All tests were passed




Server wird beendet - Lösche Semaphor 50004000.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:54.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.17
p-value of test                       :    0.9963

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:14.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9934

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.08
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.90
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.88
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6991.19
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.98
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.67
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4927.30
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908128
  j =  2                              :            45930
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908090
  j =  2                              :            45949
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:19.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.20e-3
p-value of test                       :    0.9966

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  6.4e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.17
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.17
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.84
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17187.32
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.59
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.41
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.78
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.53
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.38
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.72
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.95
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.77
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.34
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.18
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.98
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.10
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.46
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.02
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.70
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.99
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.88
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.10
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.060
p-value of test                       :    0.48

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.58e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.49e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.51
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.61
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.35
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.19
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9797.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.41
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.72
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:20.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.20
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.98
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.96
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.84
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000015379

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.70
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999909878

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.49
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    2.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.74
p-value of test                       :    0.77

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:00.65

 All tests were passed




Server wird beendet - Lösche Semaphor 51085344.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7215
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:06.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    3.32
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.96
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.93
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6962.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.67
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.35
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.46
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:58.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46002
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870002
  j =  1                              :        399907998
  j =  2                              :            45998
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908248
  j =  2                              :            45861
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:32.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.63e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.70
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.25
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.93
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.64
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.73
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.87
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.15
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17461.73
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.51
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.29
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.36
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.78
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.93
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.74
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.51
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.52
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.91
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.39
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.46
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.28
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.48
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.17
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.07
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.52
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.20
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.90
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:25.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.65
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.92e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.10
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10153.82
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9992.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5087.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11590.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:34.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.83
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000149314

Normal statistic for number of bits   :    1.18
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.21
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000090541

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.92
p-value of test                       :    0.03

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:00.17

 All tests were passed




Server wird beendet - Lösche Semaphor 52002848.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:58.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:44.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:12.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:13.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.00
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    5.80
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:43.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.04
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.71
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.05
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.34
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1546.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.08
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.03
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45858
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869858
  j =  1                              :        399908286
  j =  2                              :            45854
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46448
p-value of test                       :  4.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870448
  j =  1                              :        399907106
  j =  2                              :            46444
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
p-value of test                       :    0.9976

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.21e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.05e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.91e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.19
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:45.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.03
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:49.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.57
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.89
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.42
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.93
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.92
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.64
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.34
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.18
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.99
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.48
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.57
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.01
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.92
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.84
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.97
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.14
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.43
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.71
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -2.23
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.16e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.42e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.03
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.38
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.21
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:17.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10117.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10055.20
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:37.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4048.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:32.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.42
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.84
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999979256

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.57
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999940349

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:11.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.48
p-value of test                       :    0.93

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:10.04

 All tests were passed




Server wird beendet - Lösche Semaphor 53051424.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:52.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:57.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7191
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:10.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7268
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:14.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9969

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.25
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.83
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1522.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6961.30
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.53
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.03
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:43.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5200.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908637
  j =  2                              :            45677
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45384
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869384
  j =  1                              :        399909237
  j =  2                              :            45374
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9932

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.72e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 3.77e-4
p-value of test                       :  3.4e-3

Anderson-Darling statistic = A2       :    6.49
p-value of test                       :  5.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.07e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.27
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.97
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.18
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.08
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.78
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9943

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.47
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.24
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.22
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.04
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.33
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.64
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.97
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.52
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.78
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.14
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.80
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4820.19
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.59
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.83
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:25.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.71
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:26.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.01e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.80
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.10
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:04:27.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3953.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.80
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.38
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11906.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.67
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000081757

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000091864

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    2.69
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.54e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.31
p-value of test                       :    0.01

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:07.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               5.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54329376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1433
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334553
  j =  1                              :        599997134
  j =  2                              :             1433
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4265
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:58.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:09.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     645
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.62
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:42.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.14
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.92
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.65
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.88
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-3
p-value of test                       :    0.9973

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.99
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.89
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.42
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:59.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908054
  j =  2                              :            45964
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45581
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869581
  j =  1                              :        399908840
  j =  2                              :            45577
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.39
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.04
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.05
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17356.67
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.76
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.30
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.91
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.23
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.03
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.43
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.40
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.23
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.29
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.15
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.52
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.96
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.20
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.07
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.00
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.08
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.37
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.90
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.04
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.79e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.65
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.30
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9945.88
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:15.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4872.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.91
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.03
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11697.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.76
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000051565

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.30
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999909275

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.91

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:31.65

 All tests were passed




Server wird beendet - Lösche Semaphor 55377952.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:41.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4412
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    2.05
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.19
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.86
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.70
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.76
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.61
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   87.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:03:09.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.07
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.63
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.16
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46245
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870245
  j =  1                              :        399907511
  j =  2                              :            46243
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908310
  j =  2                              :            45839
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 3.84e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.87e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:43.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.50
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.27
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.58
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.95
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.65
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.02
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.81
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17238.55
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.71
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   45.07
p-value of test                       :  8.2e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.55
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.85
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.08
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.97
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.12
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.66
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  444.35
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.44
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.43
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.84
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.64
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.96
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.76
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.23
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.98
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.39
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.25
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 7.43e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.55
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.77
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.45
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.26
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4727.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.00
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4215.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11966.64
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.04
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.26
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000020284

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.88
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000057799

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.75
p-value of test                       :    0.96

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    3.27
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.26
p-value of test                       :    0.01

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.79

 All tests were passed




Server wird beendet - Lösche Semaphor 56426528.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9979


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:56.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4198
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4106
p-value of test                       :    0.9998    *****


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:01.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:06.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.83
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.19
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.9913

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.34
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.96
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    4.20
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:02:47.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.87
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  448.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7006.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4933.02
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:59.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908672
  j =  2                              :            45658
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45968
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869968
  j =  1                              :        399908067
  j =  2                              :            45962
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 8.27e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:49.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.46
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.48
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.81
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.71
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17699.11
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.77
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.18
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.46
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.64
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.67
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.67
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.50
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.26
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4823.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.01
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5104.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.79
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.25
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -2.26
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.20e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.35
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.09
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10174.13
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9837.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:14.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.83
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11984.43
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.82
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999968942

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.79
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000126793

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:50.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57376800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5472
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:09.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    3.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.92
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.08
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:47.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.27
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.25
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7128.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.25
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.69
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.23
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.43
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:59.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908225
  j =  2                              :            45877
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908604
  j =  2                              :            45695
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.39e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.88e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.37e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 4.96e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.92
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.68
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.14
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.03
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17543.00
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.38
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.91
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.54
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.89
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.15
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.58
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.98
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  112.14
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.49
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.95
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.11
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.51
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  242.58
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.88
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.73
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.70
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.43
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.59
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -3.66
p-value of test                       :    0.9999    *****



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.86e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 6.03e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.36
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:05.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.054
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:17.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12291.77
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.93
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000065836

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.10
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000126526

Normal statistic for number of bits   :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.31
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 81  LinearComp, r = 29              0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58425376.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4245
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4247
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:08.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7556
p-value of test                       :  2.9e-3


-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    2.42
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     825
p-value of test                       :    0.9940

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:02:44.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.10
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.40
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.09
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7222.89
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.02
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.92
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.5e-4    *****


-----------------------------------------------
CPU time used                    :  00:02:54.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907929
  j =  2                              :            46031
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46080
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870080
  j =  1                              :        399907842
  j =  2                              :            46076
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:30.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.62e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.90e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.50
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.44
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:39.69

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17694.59
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.53
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.88
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.91
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.40
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.06
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.31
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.86
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.49
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.41
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.13
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  305.33
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.68
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.65
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.19
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.44
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.00
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.33
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4861.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.87
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.29
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.47
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.01
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.68e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.39e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.79
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :  3.4e-4    *****

Anderson-Darling statistic = A2       :    7.36
p-value of test                       :  2.5e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  275.56
p-value of test                       :  3.2e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.64
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10284.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.81
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.77
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:19.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5082.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4237.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4241.58
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.31
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.36
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000003727

Normal statistic for number of bits   :   0.029
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.86
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999913322

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.47
p-value of test                       :    0.07

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.43e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:22.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 43  Permutation, t = 10             3.5e-4
 88  PeriodsInStrings, r = 0         3.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59441184.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5314
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:03.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    3.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     647
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.44
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:43.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.18
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.15
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.16
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  506.47
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.21
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.42
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5011.39
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:55.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908650
  j =  2                              :            45672
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908193
  j =  2                              :            45899
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:30.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.06

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.07e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 3.13e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:44.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.58
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.50e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17509.12
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.90
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.63
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.33
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.54
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.51
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.68
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.69
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.19
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.11
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.41
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.87
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.12
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.28
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.64
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.04
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.50
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.22
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.46
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:26.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.28
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 8.16e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.41e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.18e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.72
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.44
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.70
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9921.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10091.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.021
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:21.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5137.61
p-value of test                       :  6.8e-3

-----------------------------------------------
CPU time used                    :  00:01:55.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4172.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.03
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.16
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.10
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000047620

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.27
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000064228

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.042
p-value of test                       :    0.52

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:55.95

 All tests were passed




Server wird beendet - Lösche Semaphor 60391456.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:59.23

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4187
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:48.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.08
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.81
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.10
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.37
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.45
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.26
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.86
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.27
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.46
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5149.15
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46095
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870095
  j =  1                              :        399907811
  j =  2                              :            46093
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907997
  j =  2                              :            45991
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.9938

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.38e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.41e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.03
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.94
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.54
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:48.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.21
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.10
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17599.39
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.28
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.38
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.78
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.86
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.72
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.77
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.30
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.90
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.93
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.96
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.09
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.50
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.55

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.59
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.13
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.29
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.15
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.72
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.59
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.10
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  310.48
p-value of test                       :    0.9953


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.05
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-4
p-value of test                       :    0.9993    *****

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    4.05
p-value of test                       :  8.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.91
p-value of test                       :  1.8e-3

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 6.93e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.98
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.97
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10040.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.09
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:19.04

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4952.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4192.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.47
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.92
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.40
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999974570

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.01
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000000595

Normal statistic for number of bits   : 4.70e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.73

 All tests were passed




Server wird beendet - Lösche Semaphor 61374496.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.48

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:58.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     653
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     334
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:13.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.77
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.65
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.64
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.60
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.14
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7123.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.40
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:03:09.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.19
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5012.97
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:21.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45924
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869924
  j =  1                              :        399908157
  j =  2                              :            45914
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45375
p-value of test                       :    0.9908


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869375
  j =  1                              :        399909253
  j =  2                              :            45369
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.30

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.38e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.065
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.023
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.92

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.83
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.11
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.30
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.57
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.87
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.62
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.31
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.52
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.65
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.92
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.52
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.05
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.84
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.31
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.97
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.44
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.83
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.78
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.55
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.71
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  330.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.96
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.86
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.53
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.01
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:24.65

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.48e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.03e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.78
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.70

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.44e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  250.67
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:02:04.39

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.56
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:01.64

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 3.22e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4693.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4886.71
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3859.02
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:20.67

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.94

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.21
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999833471

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.25
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000178222

Normal statistic for number of bits   :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:01.13

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:




***********************************************************
HOST = n94, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.02

 All tests were passed




Server wird beendet - Lösche Semaphor 62357536.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5338
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.73
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.35
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:33.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.79
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.76
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.99
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7060.32
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.21
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   87.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45694
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869694
  j =  1                              :        399908614
  j =  2                              :            45690
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45672
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869672
  j =  1                              :        399908662
  j =  2                              :            45660
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:28.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.08e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    6.36
p-value of test                       :  6.9e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.62e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:40.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.23
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.05
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.56
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.85
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17243.73
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.83
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.38
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.94
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.97
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.50
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   35.79
p-value of test                       :  4.9e-3


-----------------------------------------------
CPU time used                    :  00:00:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.36
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   93.83
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.01
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.39
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:48.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.28
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.20
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5043.10
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  300.97
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.91
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.45
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.10
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.038
p-value of test                       :    0.52

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.89e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.87
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.65
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:11.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.2e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5117.47
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3970.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.61
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.42
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.10
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000034207

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.90
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999986495

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:30.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:37.10
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 49  MaxOft, t = 32                  1.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 41943040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7535
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:03:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7190
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     939
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.13
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.11
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.96
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.45
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6900.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:05.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.22
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908274
  j =  2                              :            45857
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45781
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869781
  j =  1                              :        399908439
  j =  2                              :            45779
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:29.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.72e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.81
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.92
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.30
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17389.60
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.12
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.25
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:40.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.90
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.67
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.37
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  438.97
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.68
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.98
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.42
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.48
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.65
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.20
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.52
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.30
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.29
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.21
p-value of test                       :    0.99

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.39e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.78
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:12.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.67
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10063.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4729.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.58
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.78
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.82
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999948704

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.24
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999996152

Normal statistic for number of bits   :  -0.030
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    0.22
p-value of test                       :    0.9913

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:21.28

 All tests were passed




Server wird beendet - Lösche Semaphor 43679744.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.15
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     541
p-value of test                       :    0.9923

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.32
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.74
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.51
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.74
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1462.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7138.64
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.69
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.55
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.61
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4906.27
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:32.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:25.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45782
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869782
  j =  1                              :        399908439
  j =  2                              :            45776
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907765
  j =  2                              :            46116
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:31.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:20.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.42
p-value of test                       :    0.9923

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.01
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.81
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17394.05
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.61
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.58
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.91
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.54
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.10
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.99
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.47
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  558.05
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.93
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.11
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.83
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.96
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.12
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.05
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.66
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.01
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.14
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.74
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.08
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.51
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.78
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:20.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.41
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.62
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9870.74
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:11.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5098.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.82
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.58
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999960260

Normal statistic for number of bits   :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.04
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000146083

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.98

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:57.69

 All tests were passed




Server wird beendet - Lösche Semaphor 44400640.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:51.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5229
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:38.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9938

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    3.70
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.81
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.22
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.72
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.48
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.04
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.70
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.74
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:47.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.53
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.40
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:02.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45931
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869931
  j =  1                              :        399908142
  j =  2                              :            45923
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45645
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869645
  j =  1                              :        399908717
  j =  2                              :            45631
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.70e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.46e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.14
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.95
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.71
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.20
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.05
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.31
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17320.92
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.09
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.71
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.25
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.96
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.35
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.49
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.73
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.17
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.88
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.16
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.60
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.17
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.24
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.73
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.88
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.58
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.79
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :    1.61
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:20.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.092
p-value of test                       :    0.46

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.31e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.33
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10137.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.95
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:11.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.60
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.48
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.00
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.38
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11663.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.86
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.67
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000036664

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.86
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000225232

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:13.96

 All tests were passed




Server wird beendet - Lösche Semaphor 45318144.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.29
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.70
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.69
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.54
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:14.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.29
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.96
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:05.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:47.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.62
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908467
  j =  2                              :            45762
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908225
  j =  2                              :            45877
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 2.41e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.31e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.00e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.057
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.31
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.36
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.20
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.64
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.82
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.84
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.50
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.32
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.55
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.90
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.70
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.33
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.00
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.80
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.62
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.04
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.95
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.62
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.35
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.71
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.95
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.67
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.21
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.71
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:20.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    2.49
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.16e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10136.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:11.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.16
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.54
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.30
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999923252

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.43
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000111205

Normal statistic for number of bits   :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:14.73

 All tests were passed




Server wird beendet - Lösche Semaphor 46301184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5503
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:40.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.98
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.46
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.27
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.74
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.27
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6938.04
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:20.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.87
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4991.91
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:58.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45847
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869847
  j =  1                              :        399908308
  j =  2                              :            45843
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46285
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870285
  j =  1                              :        399907432
  j =  2                              :            46281
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:31.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.89e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.79
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  116.85
p-value of test                       :  1.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.82
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.28
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:41.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.16
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.19
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.15
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.08
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.00
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.26
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.06
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.76
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.88
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.94
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.92
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.42
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.93
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.73
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.40
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4785.57
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.30
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.89
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.05
p-value of test                       :    0.70


-----------------------------------------------
Normal statistic for number of jumps  :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.60
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.35

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.10
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.98
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10103.45
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4258.72
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4163.75
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.31
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.36
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999861449

Normal statistic for number of bits   :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.11
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000097018

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.19
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:01:13.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:19.35
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 61  WeightDistrib, r = 28           1.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47349760.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.69
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9961

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.74
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.54
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.31
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.47
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  277.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.86
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.15
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:05.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.87
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.46
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5087.86
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:54.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46191
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870191
  j =  1                              :        399907620
  j =  2                              :            46187
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908332
  j =  2                              :            45825
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.93e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.089
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.94
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.77
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.61
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.60
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17420.85
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.95
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.03
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.16
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.94
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.40
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.71
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.75
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   50.18
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.64
p-value of test                       :  7.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.86
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.54
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.65
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.47
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.73
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.65
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.42
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.75
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.27
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.37
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.47
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.06e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.77e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.90
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.91
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.66
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9973.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:11.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4966.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.23
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.83
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.99
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11988.40
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.50
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000090391

Normal statistic for number of bits   :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.49
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  7999999059

Normal statistic for number of bits   : -7.44e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.089
p-value of test                       :    0.54

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.35
p-value of test                       :  9.3e-3

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:10.90

 All tests were passed




Server wird beendet - Lösche Semaphor 48529408.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4212
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4218
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7160
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7178
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.55
p-value of test                       :  5.9e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    3.53
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.11
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.86
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:19.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.74
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.59
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  491.50
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1499.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6926.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.95e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.71
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.9e-3

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:05.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.43
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.58
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.44
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:56.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45907
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869907
  j =  1                              :        399908189
  j =  2                              :            45901
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46161
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870161
  j =  1                              :        399907683
  j =  2                              :            46151
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.17e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.85e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.52e-4
p-value of test                       :  7.1e-3

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:41.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.01
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.17
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.60
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.12
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17688.16
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.82
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.74
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.81
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.80
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.54
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.74
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.33
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.27
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.60
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.44
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.11
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.86
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.63
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.50
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.61
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.98
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  329.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.98
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.73
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 3.88e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.69e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.43e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.64
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.03e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.66
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9902.06
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3887.58
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11959.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11892.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.24
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999918656

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.35
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000029134

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.61
p-value of test                       :    0.95

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:11.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:28.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NP, t = 9            5.9e-4
 84  Fourier3, r = 0                 0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49479680.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5462
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:46.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.30
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1399.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6834.92
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.34
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:03:06.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.12
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.63
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.85
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:55.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45985
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869985
  j =  1                              :        399908031
  j =  2                              :            45983
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908044
  j =  2                              :            45969
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.34e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.23
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.20
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.24
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :16994.04
p-value of test                       :    0.9906



-----------------------------------------------
CPU time used                    :  00:00:52.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.82
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.91
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.66
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  582.33
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.61
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.00
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.35
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.16
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.50
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.13
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.54
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.74
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5188.93
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.71
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.84
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.10
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    2.52
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.80
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.92
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.9923

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  7.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9607.17
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.57
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.95
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.18
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12033.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:30.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.59
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000031249

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.24
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999999836

Normal statistic for number of bits   : -1.30e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:11.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:00.39

 All tests were passed




Server wird beendet - Lösche Semaphor 50462720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5395
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7189
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.04
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.12
p-value of test                       :    0.9998    *****

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.10
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   37.26
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.94
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.98
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.38
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.22
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.77
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4947.27
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908030
  j =  2                              :            45979
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907862
  j =  2                              :            46063
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.86e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.40
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.08
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.48
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.92
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.86
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.20
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.36
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.75
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.21
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.79
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.44
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.97
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.51
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.35
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.86
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.75
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  470.73
p-value of test                       :  1.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.75
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.05
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.53
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.97
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.06
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:34.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.86
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.61
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.34e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.52
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.98
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.03
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4813.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4337.38
p-value of test                       :  8.3e-3

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4343.40
p-value of test                       :  7.0e-3

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.56
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11762.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.80
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999874859

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.66
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999759944

Normal statistic for number of bits   :   -1.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:47.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51511296.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1462
p-value of test                       :  4.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334582
  j =  1                              :        599997076
  j =  2                              :             1462
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4450
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.60
p-value of test                       :  4.7e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    2.91
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:47.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.35
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.36
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.12
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.26
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7278.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.43
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:20.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.67
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.52
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45763
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869763
  j =  1                              :        399908477
  j =  2                              :            45757
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45667
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869667
  j =  1                              :        399908669
  j =  2                              :            45661
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.16e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.38e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.51
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.51
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.24
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17464.11
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.29
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.16
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.15
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.71
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.37
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.48
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.46
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.81
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.82
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.00
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.29
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  457.95
p-value of test                       :  5.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.99
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.64
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.69
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.18
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.97
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.00
p-value of test                       :    0.98

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.87e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 7.59e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9843.76
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.22
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12045.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.09
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999989750

Normal statistic for number of bits   :  -0.081
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.81
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999885113

Normal statistic for number of bits   :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.79
p-value of test                       :    0.96

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.59
p-value of test                       :    0.06

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:26.54

 All tests were passed




Server wird beendet - Lösche Semaphor 52559872.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1458
p-value of test                       :  6.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334578
  j =  1                              :        599997084
  j =  2                              :             1458
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     640
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.51
p-value of test                       :    0.9910

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.55
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6932.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.14
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:05.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.02
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:34.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5124.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:54.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46203
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870203
  j =  1                              :        399907595
  j =  2                              :            46201
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 6.23e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.84e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 9.02e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.072
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.33
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.54
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:54.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.44
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.24
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17846.36
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.92
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.94
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.56
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.34
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.78
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.31
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.74
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.19
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.47
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.40
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.53
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.41
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.17
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  439.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.70
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.35
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.66
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.67
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.75
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.68
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.50
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.41
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.76
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.81
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.99
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :   -1.58
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.44
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   34.05
p-value of test                       :  4.0e-5    *****

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.11
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9841.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.00
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -3.30
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.14e-3
p-value of test                       :    0.9968

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.84
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11818.94
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   86.17
p-value of test                       :  3.5e-3


-----------------------------------------------
Total number of bits:  7999941108

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.43
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000086188

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    2.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.82
p-value of test                       :    0.97

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:47.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 87  LongestHeadRun, r = 27          4.0e-5
 93  HammingCorr, L = 300            0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53706752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     836
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    2.95
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.80
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  265.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.37
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.69
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.46
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5186.38
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:55.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45993
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869993
  j =  1                              :        399908017
  j =  2                              :            45987
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46037
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870037
  j =  1                              :        399907934
  j =  2                              :            46021
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  5.5e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 9.05e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  3.7e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.20e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.17
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.63
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.12
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.24
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.51
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.71
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.74
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.96
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.53
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.77
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5251.22
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.85
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.10
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.46
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.53
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.66
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.95
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.92
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.61e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.85e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.36
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.58
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.59
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:15.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.86
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.69
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4285.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:33.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11756.77
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.40
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000116608

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.76
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999863150

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.088
p-value of test                       :    0.54

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:12.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:04.39
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 50  SampleProd, t = 8               0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54722560.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1228
p-value of test                       : 1 -  9.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334348
  j =  1                              :        599997544
  j =  2                              :             1228
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.38
p-value of test                       :  5.8e-3

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     559
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:13.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     170
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.50
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.02
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.59
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  197.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  501.97
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1497.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7013.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.1e-3

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:21.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.87
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5143.71
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  5.7e-3


-----------------------------------------------
CPU time used                    :  00:02:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908388
  j =  2                              :            45803
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45297
p-value of test                       :    0.9968


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869297
  j =  1                              :        399909408
  j =  2                              :            45293
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:31.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.54
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.98
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.55
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17105.11
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.02
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.89
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.10
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   64.12
p-value of test                       :  2.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.07
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.69
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.17
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.94
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.62
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.79
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.96
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.76
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.14
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.01
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.30
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.64
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.57
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.46
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.08
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.96
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.03e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.49
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.58
p-value of test                       :    0.9912

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.55
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.89
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.62
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4035.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4091.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11804.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.52
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.23
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000072580

Normal statistic for number of bits   :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.84
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000128224

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:04.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  3  CollisionOver, t = 2           1 -  9.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55771136.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:49.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1453
p-value of test                       :  8.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334573
  j =  1                              :        599997094
  j =  2                              :             1453
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5249
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:03:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:40.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7474
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9971


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.58
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.03
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.03
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:05.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.17
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.76
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:57.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45521
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869521
  j =  1                              :        399908961
  j =  2                              :            45515
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45892
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869892
  j =  1                              :        399908220
  j =  2                              :            45884
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.29e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.37
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.55
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.42
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.32
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.42
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.54
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.88
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.69
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.26
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.77
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.39
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.87
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.17
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4855.68
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.66
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.33
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.40
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :   -1.71
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.42e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.22
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.00
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.69
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9741.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.37
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4704.52
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.63
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.09
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.73
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000124402

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.54
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999941468

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   0.032
p-value of test                       :    0.49

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.9902

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.86
p-value of test                       :    0.97

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.72e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:29.62

 All tests were passed




Server wird beendet - Lösche Semaphor 57081856.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  6.1e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    6958
p-value of test                       : 1 -  1.1e-5    *****


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7114
p-value of test                       :    0.9916


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     888
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     278
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.17
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.97
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.00
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   40.08
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.89
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1498.35
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7052.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:06.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.75
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:47.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.29
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.78
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908198
  j =  2                              :            45898
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907703
  j =  2                              :            46141
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:48.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.0e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 5.61e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.025
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.93
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.15
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.23
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.49
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.01
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.81
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.73
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.26
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.86
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.74
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.42
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.27
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.43
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.93
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.77
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.10
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.09
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.34
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.45
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5084.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  367.78
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.95
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.05
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5105.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.91
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:34.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.49
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.65
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.76e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10092.86
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11791.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:29.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.09
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999959534

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.10
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999908096

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.76
p-value of test                       :    0.04

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:07.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  1  SerialOver, r = 0               6.1e-4
 20  BirthdaySpacings, t = 16       1 -  1.1e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58097664.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    3.14
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9953

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   32.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   77.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:06.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.55
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.15
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:35.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5254.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:55.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908629
  j =  2                              :            45675
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908208
  j =  2                              :            45890
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:01:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.28e-3
p-value of test                       :    0.9965

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.23
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.26
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  154.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17504.76
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.02
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.37
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.35
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.93
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.10
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.24
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.55
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.95
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.03
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.89
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.98
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.10
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.80
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.81
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.10
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.65
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.33e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.97
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.14
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.58
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.75
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:04:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11720.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.51
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999901814

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000091717

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:35.55

 All tests were passed




Server wird beendet - Lösche Semaphor 59080704.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7511
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.62
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.92
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.24
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.22
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.14
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  425.23
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6964.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.56
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.13
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:34.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.23
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.02
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.81
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:54.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46127
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870127
  j =  1                              :        399907748
  j =  2                              :            46123
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45842
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869842
  j =  1                              :        399908320
  j =  2                              :            45834
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:31.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:19.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.55e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.41e-4
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    : 4.92e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.43
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.81
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.01
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.98
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.52
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:41.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.17
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.50
p-value of test                       :    0.9951


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.66
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.13
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.70
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.41
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.11
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  106.90
p-value of test                       :  7.4e-3


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.42
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.55
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.43
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.82
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  323.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.41
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.08
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.80
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 9.58e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.07
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.51
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.15
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.28
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.44
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:04:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.43
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11965.69
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.86
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000070630

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.63
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000031495

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.23
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:30.45

 All tests were passed




Server wird beendet - Lösche Semaphor 60030976.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.13
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.86
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:01.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.41
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.58
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.22
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.70
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.33
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.42
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.00
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.03
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4982.50
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:01.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908873
  j =  2                              :            45556
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46204
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870204
  j =  1                              :        399907595
  j =  2                              :            46198
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 8.88e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-5
p-value of test                       : 1 -  9.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.66
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.60
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:41.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17642.98
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.35
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   40.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.92
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.64
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.84
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.19
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.96
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.40
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  552.12
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.46
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.26
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.98
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4976.25
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.07
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.53
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.88
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5016.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.88
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.53
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.88
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.15
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.06
p-value of test                       :    0.14

Sample variance                       :    2.41
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.23
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.62
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.66
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.26
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9944.89
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4679.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4808.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4122.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4219.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.06
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11971.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.49
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999959309

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.81
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999882653

Normal statistic for number of bits   :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    2.22
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:43.12

 All tests were passed




Server wird beendet - Lösche Semaphor 61243392.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4193
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4169
p-value of test                       :    0.9947


-----------------------------------------------
CPU time used                    :  00:01:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7207
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    4.29
p-value of test                       :  6.3e-3

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.36
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.83
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.21
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.77
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.69
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.21
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  462.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1295.16
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:02:12.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7131.36
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.91
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.25
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:41.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.53
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:18.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46076
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870076
  j =  1                              :        399907853
  j =  2                              :            46066
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46177
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870177
  j =  1                              :        399907651
  j =  2                              :            46167
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.9e-3

Anderson-Darling statistic = A2       :    3.50
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.96e-3
p-value of test                       :    0.9915

Anderson-Darling statistic = A2       :    2.69
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.23e-3
p-value of test                       :    0.9904

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 9.54e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.46
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.24
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.34
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.78
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17624.24
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.44
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.10
p-value of test                       :  6.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.46
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.48
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.66
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.96
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.57
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.72
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.07
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  112.26
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.16
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.37
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.29
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.80
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4985.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.58
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.24
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.38
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5112.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  268.60
p-value of test                       :  8.6e-4    *****


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.94
p-value of test                       :    0.79


-----------------------------------------------
Normal statistic for number of jumps  :   -0.96
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.01
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.36e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.94
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.27
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:01.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.55
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9881.74
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:01.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.06
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.30
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.06
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.03
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  8000029005

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.54
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999984464

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.26
p-value of test                       :    0.99

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   8.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62423040.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5336
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7475
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     616
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.75
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.05
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:11.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.50
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.58
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.64
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.62
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   13.33
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.45
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.80
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.94
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.65
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:13.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46185
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870185
  j =  1                              :        399907635
  j =  2                              :            46175
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907921
  j =  2                              :            46035
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:34.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.41e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.81
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.95
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.30
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.15
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.66
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.40
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17317.80
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.90
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.55
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.87
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   16.04
p-value of test                       :    0.9984


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.12
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.42
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.98
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.40
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5094.03
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.80
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.12
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.60
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  454.00
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.34
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.29
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:13.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.37
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.97e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.32
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:11.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.03
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.94
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4850.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.27
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11757.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12044.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.11
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000100897

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.23
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  8000108703

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    4.11
p-value of test                       :  8.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.2e-3

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:38.70

 All tests were passed




Server wird beendet - Lösche Semaphor 41975809.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:47.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5312
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.21
p-value of test                       :  7.0e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:11.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.44
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.00
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1502.05
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.54
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.64
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.90
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5175.68
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:20.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46075
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870075
  j =  1                              :        399907855
  j =  2                              :            46065
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908357
  j =  2                              :            45820
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.93e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 5.42e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.56
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.92
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.67
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.83
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17301.93
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.84
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.86
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.01
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.39
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.02
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.21
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.09
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.24
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.27
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.88
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.52
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.58
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.53
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.83
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.88
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    2.34
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.38e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.00
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.56
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9816.08
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:04:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  1.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    6.37
p-value of test                       :  7.1e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4603.41
p-value of test                       :    0.9984

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.34
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4012.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11944.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11719.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.75
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000031009

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.85
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000063328

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:45.40

 All tests were passed




Server wird beendet - Lösche Semaphor 43646977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.84
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.49
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.06
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.92
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.22
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.97
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.31
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.78
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.46
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:09.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45622
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869622
  j =  1                              :        399908758
  j =  2                              :            45618
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45623
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869623
  j =  1                              :        399908762
  j =  2                              :            45607
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9966

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9930


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 6.51e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.70e-6
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    : 3.09e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.74
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.07
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.96
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.77
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.17
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17693.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.01
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.87
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.09
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.28
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.63
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.74
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.35
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.63
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.19
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.93
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.98
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.08
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.96
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.02
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.64
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.12
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.96
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.83
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.85
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.61
p-value of test                       :    0.05

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 6.72e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.79
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.22
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.94
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.51
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9951.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.87
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:04:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.80
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4236.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12032.41
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11908.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:32.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.45
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999890348

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.29
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000014413

Normal statistic for number of bits   :    0.11
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:11.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:39.96

 All tests were passed




Server wird beendet - Lösche Semaphor 44793857.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:50.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4171
p-value of test                       :    0.9942


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    4.67
p-value of test                       :  4.1e-3

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.89
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.45
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.26
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.08
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.43
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  206.54
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.07
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:03:16.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.35
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5051.22
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908686
  j =  2                              :            45651
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908322
  j =  2                              :            45836
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:10.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:20.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.99e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.56
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.83
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17611.32
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.89
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.80
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.09
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.57
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.98
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.10
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.16
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.63
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.42
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.15
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.39
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.45
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.97
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.56
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.73
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.27
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.56
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.45
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.94e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.87
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9858.51
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10259.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:04:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 2.12e-3
p-value of test                       :    0.9978

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4725.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.93
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11508.47
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.15
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.20
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000167794

Normal statistic for number of bits   :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.29
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999905018

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    3.20
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    3.00
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.12
p-value of test                       :    0.02

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:58.70

 All tests were passed




Server wird beendet - Lösche Semaphor 45613057.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5299
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     601
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9924

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.52
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6826.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:52.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.81
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:11.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.17
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.44
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5189.63
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:59.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908023
  j =  2                              :            45981
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908333
  j =  2                              :            45823
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.82e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 3.34e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.64e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.43
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.97
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.24
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17248.66
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.04
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.52
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.68
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.53
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.60
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.11
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.01
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.07
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.15
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.47
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.51
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.86
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.42
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.81
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.31
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.15
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.065
p-value of test                       :    0.53

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.63e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 6.77e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.80
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.69
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.68
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.89
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4884.40
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.32
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.42
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.02
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000054025

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.02
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000019360

Normal statistic for number of bits   :    0.15
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:32.86

 All tests were passed




Server wird beendet - Lösche Semaphor 46923777.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1255
p-value of test                       :    0.9986

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334375
  j =  1                              :        599997490
  j =  2                              :             1255
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.98
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    3.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.43
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.15
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.84
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.35
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  220.22
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.80
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7361.05
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.43
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.69
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5154.26
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:05.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45439
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869439
  j =  1                              :        399909129
  j =  2                              :            45425
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908061
  j =  2                              :            45965
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:30.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.67e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.10e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.60
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.49
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.65
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17614.42
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.24
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.75
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.98
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.62
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.04
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.37
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.14
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.53
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.98
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.08
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.16
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.57
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.68
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.69
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.73
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.57
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.33
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.45
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.13
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.48
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.96
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.46
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.049
p-value of test                       :    0.48

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.73e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.54
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.49
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10192.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.30
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.10
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.36
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999910289

Normal statistic for number of bits   :   -0.71
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.56
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999932465

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:33.25

 All tests were passed




Server wird beendet - Lösche Semaphor 47874049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:52.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5584
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:11.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:13.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     930
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.31
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.78
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.64
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:29.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.29
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7235.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.55
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  3.9e-3


-----------------------------------------------
CPU time used                    :  00:03:04.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907578
  j =  2                              :            46205
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:30.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.83e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.46
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.76
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.28
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.99
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.02
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.97
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.14
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.32
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.56
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.56
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.48
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.28
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.55
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.42
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.24
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.27
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.67
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.28
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.19
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  423.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.08
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.25
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4873.24
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.56
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.33
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.78
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.74
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.098
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.29
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.63
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10090.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:31.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.15
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11979.72
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.06
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  8000085969

Normal statistic for number of bits   :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.34
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999935570

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.66
p-value of test                       :    0.05

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.21

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:54.61

 All tests were passed




Server wird beendet - Lösche Semaphor 48857089.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5519
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7572
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.83
p-value of test                       :  3.7e-3

Test on the Nm values of W_{n,i}(mNP1):    9.56
p-value of test                       :  2.3e-5    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     363
p-value of test                       :  2.3e-4    *****

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    2.20
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.60
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.58
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.79
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1329.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.26
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:46.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.31
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5105.41
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46296
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870296
  j =  1                              :        399907412
  j =  2                              :            46288
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45854
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869854
  j =  1                              :        399908297
  j =  2                              :            45844
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:31.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  8.3e-3

Anderson-Darling statistic = A2       :    4.01
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.09e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.17e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.23
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.99
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.02
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.51
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.27
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17592.57
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.88
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.42
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.48
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.97
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.61
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.05
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.40
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.57
p-value of test                       :    0.9955


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.63
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.64
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.27
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  319.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.66
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   29.35
p-value of test                       :  3.5e-3


-----------------------------------------------
Normal statistic for number of jumps  :   -2.11
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.17e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.53
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.93
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10149.13
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9961.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.070
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:33.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4971.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4073.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11750.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:34.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.01
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999996470

Normal statistic for number of bits   :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.35
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000002191

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:52.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP1, t = 9          2.3e-5
 24  ClosePairs NJumps, t = 9        2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50036737.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5484
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    3.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.15
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.51
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.91
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.09
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:20.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.66
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.44
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.33
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.33
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.96
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.74
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5174.26
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:55.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908798
  j =  2                              :            45595
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45650
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869650
  j =  1                              :        399908702
  j =  2                              :            45646
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.00e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 3.24e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.98
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.48
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.81
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.49
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.02
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.46
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17327.64
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.01
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.01
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.27
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.12
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.59
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.96
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.66
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.39
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.44
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.88
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  186.93
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.42
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.05
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.58
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4865.62
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.31
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.78
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.84
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4818.55
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.93
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.31
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.63
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.98
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    2.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.36e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.82e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.65
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.67
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.87
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9754.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:04:11.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.87
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11823.58
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.39
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999855335

Normal statistic for number of bits   :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.49
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000043216

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.057
p-value of test                       :    0.48

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:58.50

 All tests were passed




Server wird beendet - Lösche Semaphor 51281921.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.6e-3


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1451
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334571
  j =  1                              :        599997098
  j =  2                              :             1451
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1257
p-value of test                       :    0.9983

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334377
  j =  1                              :        599997486
  j =  2                              :             1257
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5405
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7216
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:04:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.98
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    3.03
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.13
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.12
p-value of test                       :    0.9928

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.93
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.50
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.59
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.59
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.40
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.71
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.52
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.53
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.01
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:55.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46218
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870218
  j =  1                              :        399907570
  j =  2                              :            46206
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45927
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869927
  j =  1                              :        399908150
  j =  2                              :            45919
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.51e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.50e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.53
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.32
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.77
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.20
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:11.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.30
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.22
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.00
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.58
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.21
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   99.27
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.29
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.63
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.82
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.43
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.26
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.72
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.65
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  458.29
p-value of test                       :  5.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.94
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.45
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.36
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.65
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.31
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.46
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.11
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.32
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.44
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.36e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.84e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.03
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.00
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:10.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.46
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4938.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.11
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.39
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.02
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999894944

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.32
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000001087

Normal statistic for number of bits   : 8.59e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:43.82

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7152
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     267
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9975

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9923

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.75
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  483.18
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7194.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.38
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:07.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.97
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.68
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.66
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908265
  j =  2                              :            45863
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908661
  j =  2                              :            45668
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.70
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.90
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.66
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.66
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9939

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.55
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.71
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17427.44
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.09
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.33
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.78
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.87
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.73
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.75
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.54
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.92
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.91
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.87
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.20
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.42
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4830.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.15
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.03
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.55
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :  -0.024
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.06e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.04e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.68
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.38
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9861.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4683.85
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5016.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.02
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:30.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.72
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000004246

Normal statistic for number of bits   :   0.034
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.93
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999944219

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:15.68

 All tests were passed




Server wird beendet - Lösche Semaphor 53182465.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5471
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7155
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:50.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.04
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   22.64
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.08
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.92
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.77
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.72
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  381.59
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6975.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.60
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.01
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   93.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4954.38
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:55.73

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46319
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870319
  j =  1                              :        399907364
  j =  2                              :            46315
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46342
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870342
  j =  1                              :        399907323
  j =  2                              :            46328
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.24
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.46
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.38
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.95
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.13
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.69
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.96
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.36
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.87
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  424.02
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.39
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.04
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.45
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4801.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.64
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.06
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.17
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5066.06
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.88
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.02
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.87
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 8.36e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.40
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.99
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.94
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : 1.55e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11541.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.97
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.88
p-value of test                       :    0.94


-----------------------------------------------
Total number of bits:  7999966686

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.77
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999938105

Normal statistic for number of bits   :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.94
p-value of test                       :  9.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9926

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.87
p-value of test                       :    0.81

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:50.68

 All tests were passed




Server wird beendet - Lösche Semaphor 54231041.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.20
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9974


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.80
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.71
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.97
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1457.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.59
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.70
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.23
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.18
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908366
  j =  2                              :            45814
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46353
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870353
  j =  1                              :        399907298
  j =  2                              :            46345
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.93e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 2.00e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.94
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.32
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.60
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.79
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9916

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:29.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.53
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17419.96
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.68
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.07
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.32
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.99
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.52
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.42
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.67
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.17
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.88
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.71
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.25
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4947.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.25
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.77
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.13
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.99
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.91
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.84
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   0.038
p-value of test                       :    0.48

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.26e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.57e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 9.76e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.30
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.11
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.69
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.94
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4279.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.74
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.55
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000100030

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.82
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000099364

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:27.10

 All tests were passed




Server wird beendet - Lösche Semaphor 55279617.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4456
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.38
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     978
p-value of test                       :  5.3e-3

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.23
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.85
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.43
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.18
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.43
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.76
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7005.47
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.44
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.58
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4996.62
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908423
  j =  2                              :            45784
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45501
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869501
  j =  1                              :        399909001
  j =  2                              :            45495
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :  3.7e-3

Anderson-Darling statistic = A2       :    4.88
p-value of test                       :  3.3e-3


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.30e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.30
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.41
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.81
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.96
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17143.92
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.96
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.57
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.44
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.59
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.27
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.90
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.34
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.82
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.47
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.36
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.76
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  541.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.98
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.10
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.18
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.86
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.05
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.26
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.73
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.74
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.80
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.34
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.73
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :   -1.54
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.90
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.31
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.68e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.84
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.45
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:32.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.44
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.79
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.98
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.70
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000003238

Normal statistic for number of bits   :   0.026
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.70
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999994022

Normal statistic for number of bits   :  -0.047
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    2.70
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:17.37

 All tests were passed




Server wird beendet - Lösche Semaphor 56328193.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4464
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.60
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.85
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.93
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.01
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.49
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7332.00
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.15
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.67
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.49
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:59.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908357
  j =  2                              :            45820
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45792
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869792
  j =  1                              :        399908418
  j =  2                              :            45788
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.88e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.54e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.03
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.50
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.08
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.43
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.98
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-3
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17872.33
p-value of test                       :  9.3e-3



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.00
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.35
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.69
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.87
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.44
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.23
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  431.88
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.22
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.37
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.82
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  428.98
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.25
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.14
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.28
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.25
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.80
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.66
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :  -0.051
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.03e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.63e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.08
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.24
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10182.74
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10188.19
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.24
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.77
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.85
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11775.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.36
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  7999978203

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.53
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999919121

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.39
p-value of test                       :    0.08

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:26.70

 All tests were passed




Server wird beendet - Lösche Semaphor 57507841.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.35
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.30
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.62
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.19
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1379.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6733.03
p-value of test                       :    0.9962

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.25
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.83
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.56
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4843.87
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:58.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908027
  j =  2                              :            45982
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908187
  j =  2                              :            45902
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 7.56e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.81e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.30
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.63
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.45
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.72
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.10
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.29
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-3
p-value of test                       :    0.9977

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.97
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.60
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.30
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.34
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.14
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.31
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.12
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.98
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.39
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.82
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.82
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.45
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.03
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.55
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.20
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.80
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -1.10
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.32e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 5.88e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.44
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.40
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.79
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.89
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10263.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.62
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4858.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4700.99
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.67
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11708.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11747.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.17
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000085276

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.21
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000009070

Normal statistic for number of bits   :   0.072
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:43.96

 All tests were passed




Server wird beendet - Lösche Semaphor 58523649.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4122
p-value of test                       :    0.9995    *****


-----------------------------------------------
CPU time used                    :  00:01:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7137
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     641
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.98
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.71
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:10.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.27
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.07
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.10
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:09.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.61
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.70
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5008.00
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908816
  j =  2                              :            45589
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908086
  j =  2                              :            45948
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:29.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.44e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.84
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.96
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.86
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 4.37e-3
p-value of test                       :    0.9955

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.00
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.66
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17416.35
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.16
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.84
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.04
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.75
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.39
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.26
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.69
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  578.63
p-value of test                       :  8.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.34
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.04
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.86
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.35
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.86
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5025.79
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.59
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  241.71
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.37
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.60
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.17
p-value of test                       :    0.99

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.83e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.18
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.14
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.49
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.64
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10126.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:12.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5039.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.36
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.34
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.47
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999972095

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.06
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000040507

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.27

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.12
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:22.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 16  BirthdaySpacings, t = 7         0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59506689.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5374
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.01
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.50
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    4.35
p-value of test                       :  5.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.91
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.28
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.82
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1405.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.10
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:29.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.51
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.74
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:04.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46146
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870146
  j =  1                              :        399907715
  j =  2                              :            46132
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45820
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869820
  j =  1                              :        399908364
  j =  2                              :            45812
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.70e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.53
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.32
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.08
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.01
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.67
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.86
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.80
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.84
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.35
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.18
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.15
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.04
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.60
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.92
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.53
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4920.69
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.84
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.01
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.59
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.96
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.58
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.99e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.68
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.02
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.79
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4997.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.21
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3931.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.33
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.63
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000010726

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.88
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000283159

Normal statistic for number of bits   :    2.24
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:11.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:34.01

 All tests were passed




Server wird beendet - Lösche Semaphor 60456961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5418
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.63
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.66
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.71
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.38
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.54
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6923.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.31
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.76
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.78
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:18.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45719
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869719
  j =  1                              :        399908564
  j =  2                              :            45715
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907766
  j =  2                              :            46114
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 2.34e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.50
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.72
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.57
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17507.29
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:00:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.67
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.84
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.53
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.83
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.93
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.73
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.35
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.69
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.26
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.36
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.61
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.31
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.75
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.33
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.48
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.81
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.64
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.21
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.04
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.26
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.48
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.065
p-value of test                       :    0.47

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.15e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 2.45e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.79
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.03
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.56
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.28
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.037
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.35
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:15.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.48
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4105.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11527.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11840.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.56
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999907886

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.43
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999921554

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.23
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.73
p-value of test                       :    0.96

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.20

 All tests were passed




Server wird beendet - Lösche Semaphor 61440001.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1283
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334403
  j =  1                              :        599997434
  j =  2                              :             1283
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5525
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4226
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.02
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.50
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.32
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.90
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.57
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.11
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.21
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7201.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:03:08.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  166.94
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4953.38
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:01.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908063
  j =  2                              :            45964
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:29.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.34e-3
p-value of test                       :    0.9986

Anderson-Darling statistic = A2       :    4.07
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.30e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.92e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.19e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.082
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.33
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.36
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.51
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.81
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.74
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.62
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17349.31
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.82
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.53
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.77
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.24
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.77
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.84
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.48
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.85
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.39
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.83
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.31
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.67
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.84
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.74
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.56
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.58
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.86
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.61
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.80
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.05
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  151.49
p-value of test                       :    0.9956


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.71
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.20
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.14e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 8.73e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.45e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.05
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.88
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9854.44
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:48.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5040.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4759.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:47.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:20.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11922.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11517.58
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.79
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999917801

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.38
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999978866

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    2.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:26.23

 All tests were passed




Server wird beendet - Lösche Semaphor 62390273.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5467
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4229
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:34.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4437
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7473
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7170
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     928
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.15
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:20.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.42
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    2.55
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     123
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.70
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.86
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.81
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1460.90
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:09.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.55
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.05
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5048.58
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45770
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869770
  j =  1                              :        399908463
  j =  2                              :            45764
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45708
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869708
  j =  1                              :        399908589
  j =  2                              :            45698
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:31.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.96e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.01e+6
p-value of test                       :  2.0e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 1.98e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.21e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:52.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.80
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.64
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.82
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:32.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17172.12
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.62
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.16
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.52
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.70
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.06
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.83
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.04
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.85
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.28
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.06
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.97
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.76
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.36
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.16
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.53
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.75
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.44
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.25
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.47
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10034.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.8e-3

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10163.22
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.22
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4043.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11639.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:31.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.72
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000059026

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.87
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999980855

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   0.018
p-value of test                       :    0.49

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:13.29

 All tests were passed




Server wird beendet - Lösche Semaphor 42008578.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.30
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.53
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.80
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.57
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.68
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.61
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.50
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.33
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.15
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.91
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45657
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869657
  j =  1                              :        399908691
  j =  2                              :            45647
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908169
  j =  2                              :            45908
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.50e-5
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    : 3.24e-4
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.35e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 6.45e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.15
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.89
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   64.78
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.58
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.91
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:31.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.44
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.22
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.25
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.43
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.46
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.25
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.11
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.22
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.13
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.50
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.72
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.53
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.40
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5195.84
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.81
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.77
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.24
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.61
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 4.78e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 7.00e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.03
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.95
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.35
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10060.89
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.42
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.73
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11652.58
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.03
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000117745

Normal statistic for number of bits   :    0.93
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.56
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000124453

Normal statistic for number of bits   :    0.98
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.40

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.08
p-value of test                       :    0.98

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    2.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:55.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43122690.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1274
p-value of test                       :    0.9929

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334394
  j =  1                              :        599997452
  j =  2                              :             1274
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:11.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     893
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    3.23
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.85
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.62
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.68
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.90
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1321.10
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7004.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.15
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.69
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5134.16
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:20.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46359
p-value of test                       :    0.01


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870359
  j =  1                              :        399907283
  j =  2                              :            46357
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45832
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869832
  j =  1                              :        399908341
  j =  2                              :            45822
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9962


-----------------------------------------------
CPU time used                    :  00:02:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.47e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.87
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.88
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.48
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.59
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.32
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17263.02
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.13
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.43
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.21
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.15
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.83
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.36
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.84
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  204.12
p-value of test                       :  1.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.17
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.37
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.80
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5162.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.97
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.98
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.43
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.48
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.34
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.86
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    2.37
p-value of test                       :  8.8e-3



-----------------------------------------------
CPU time used                    :  00:02:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.68
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    1.67
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.61e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 3.33e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.76
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.10
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.56
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.42
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.80
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.77
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.34
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11535.55
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.54
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999998207

Normal statistic for number of bits   :  -0.014
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.61
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999993824

Normal statistic for number of bits   :  -0.049
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.63
p-value of test                       :    0.74

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:19.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.37
p-value of test                       :    0.9911

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:16.87

 All tests were passed




Server wird beendet - Lösche Semaphor 44236802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:47.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5264
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:05.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:09.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.46
p-value of test                       :  1.8e-3

Test on the Nm values of W_{n,i}(mNP1):    2.39
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     856
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    3.01
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.61
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     180
p-value of test                       :  9.4e-3

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.82
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.43
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  195.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  342.86
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.20
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7195.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.12
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.94
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   97.53
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:37.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.08
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45382
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869382
  j =  1                              :        399909239
  j =  2                              :            45376
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46105
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870105
  j =  1                              :        399907790
  j =  2                              :            46105
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:31.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9911

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.43e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.036
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.45
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.49
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.94
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.80
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:42.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17438.69
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.93
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.48
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.25
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.07
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.60
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  201.05
p-value of test                       :  1.7e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.79
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.62
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.11
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.67
p-value of test                       :    0.9910


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  551.97
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.56
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.67
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.14
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.34
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.21
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.34
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.70
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.38
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.63
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.08
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.62e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.99
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.19
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3910.30
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11774.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.89
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999988553

Normal statistic for number of bits   :  -0.090
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.99
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000233641

Normal statistic for number of bits   :    1.85
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:13.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 35  Gap, r = 25                     0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45940738.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5391
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4170
p-value of test                       :    0.9944


-----------------------------------------------
CPU time used                    :  00:01:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     867
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     617
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9968

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.69
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1569.89
p-value of test                       :  7.8e-3

-----------------------------------------------
CPU time used                    :  00:02:01.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.52
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:37.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5190.32
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908558
  j =  2                              :            45718
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908071
  j =  2                              :            45963
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:30.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.49e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.82e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.85
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17513.09
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.58
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.72
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.64
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.36
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.79
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.51
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.08
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.91
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.78
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.39
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.29
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.98
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.86
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.40
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  446.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.82
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.03
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.21
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.17
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 8.67e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.95
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.78
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.31
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.92
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.78
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000038674

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.21
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  7999983978

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:57.42

 All tests were passed




Server wird beendet - Lösche Semaphor 46956546.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5346
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:39.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7246
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.38
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     830
p-value of test                       :    0.9904

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.45
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   42.05
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.51
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.31
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  181.62
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:51.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1431.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.07
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4893.41
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908388
  j =  2                              :            45803
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907538
  j =  2                              :            46225
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.57e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.14
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.02
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.54
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:19.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17604.44
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.07
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.75
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.67
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.32
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.69
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.98
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.22
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.01
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.33
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.01
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.61
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.07
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.29
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.85
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.02
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.18
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.78
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5049.02
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.45
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.03
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.68e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 8.89e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.41
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10002.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.50
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5110.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.05
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4065.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.24
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11943.73
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.76
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999971981

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.00
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000226750

Normal statistic for number of bits   :    1.79
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:12.62

 All tests were passed




Server wird beendet - Lösche Semaphor 47906818.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997175
  j =  2                              :             1411
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5496
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:40.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7485
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.48
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.63
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.46
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:30.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7041.58
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.87
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:15.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.99
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.37
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4921.17
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:05.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46284
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870284
  j =  1                              :        399907438
  j =  2                              :            46272
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46425
p-value of test                       :  5.5e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870425
  j =  1                              :        399907154
  j =  2                              :            46417
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.48
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.04
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17212.86
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.56
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.10
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.03
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.23
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.72
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.72
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.94
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.76
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.95
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.30
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.05
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.64
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.73
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.24
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4923.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.84
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.77
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.41
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.55
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.85
p-value of test                       :    0.03

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.74e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:46.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.57e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.30
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.17
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.94
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.07
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.24
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4290.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.52
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.43
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.71
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  7999876848

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.94
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000073444

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:51.02

 All tests were passed




Server wird beendet - Lösche Semaphor 48955394.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5339
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7082
p-value of test                       :    0.9972


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7452
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     909
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.92
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.87
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.19
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.60
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1532.17
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.01
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.18
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46010
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870010
  j =  1                              :        399907981
  j =  2                              :            46008
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46011
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870011
  j =  1                              :        399907980
  j =  2                              :            46007
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.07e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.09e-4
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.75e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.28
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.98
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.65
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17540.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.23
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.79
p-value of test                       :    0.9931


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.38
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.25
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.96
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.37
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.15
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.28
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.24
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.22
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.80
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5110.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.70
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -1.86
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.41
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.38e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.22
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.92e-3
p-value of test                       :    0.9980

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  159.25
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.87
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.77
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:14.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.74e-3
p-value of test                       :    0.9961

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4652.44
p-value of test                       :    0.9926

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4640.02
p-value of test                       :    0.9948

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4274.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11855.62
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12010.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.57
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000000811

Normal statistic for number of bits   : 6.41e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.15
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000099649

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :  -0.091
p-value of test                       :    0.54

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.08
p-value of test                       :    0.86

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:22.44

 All tests were passed




Server wird beendet - Lösche Semaphor 50266114.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:08.08

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:02.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4355
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.52
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.73
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.11
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.79
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.07
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.79
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1463.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7058.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.81
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5233.81
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:02:59.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45803
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869803
  j =  1                              :        399908400
  j =  2                              :            45791
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908327
  j =  2                              :            45829
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9902

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.09e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.55e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.39
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.19
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.18
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.74
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.14
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.19
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.05
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:40.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17176.89
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.65
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.22
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.03
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.09
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.36
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.66
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.37
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.51
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.08
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.06
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.47
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.63
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.11
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.44
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.88
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.84
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.39
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.98
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    2.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.63e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.59e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.71
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.34
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10243.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:15.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.32
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11914.30
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.01
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999857306

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.56
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000172630

Normal statistic for number of bits   :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.19e-3
p-value of test                       :    0.9967

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.38
p-value of test                       :    0.9914

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:35.60

 All tests were passed




Server wird beendet - Lösche Semaphor 51249154.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5327
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4153
p-value of test                       :    0.9975


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    2.32
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     633
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.69
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.82
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.94
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.07
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  471.57
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1471.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.99
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.47
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   43.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5079.69
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46261
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870261
  j =  1                              :        399907481
  j =  2                              :            46255
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45994
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869994
  j =  1                              :        399908017
  j =  2                              :            45984
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.89
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.86
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.61
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.37
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.58
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.58
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17702.09
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.68
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.78
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.74
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.95
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.91
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.52
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.90
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.72
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.20
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.98
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.97
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  316.83
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.69
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.07
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.96
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.95
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.72
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:34.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.06
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.18
p-value of test                       :    0.01

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.69e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 7.46e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.40
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10238.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.11
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.56
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3992.18
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:33.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.71
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:33.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.01
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999944105

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.02
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999852980

Normal statistic for number of bits   :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.24
p-value of test                       :    0.99

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:39.34

 All tests were passed




Server wird beendet - Lösche Semaphor 52297730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4209
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:12.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     871
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:48.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.60
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.97
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.66
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  167.22
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.75
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908140
  j =  2                              :            45924
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907973
  j =  2                              :            46012
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.29
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.81
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.20
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.03
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17233.71
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.28
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.97
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.67
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.13
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.35
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.25
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.11
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.13
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.58
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.66
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.50
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.19
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.59
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.54
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.97
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.29
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.86
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.50
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.04
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4927.24
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.90
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.05
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.65
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :  -0.060
p-value of test                       :    0.52

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.25
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:34.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.21
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.34
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9900.78
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.53
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.030
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:04:32.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.04
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.95
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.98
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999941405

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.78
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000077257

Normal statistic for number of bits   :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    1.73
p-value of test                       :    0.04

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    2.42
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:14.57

 All tests were passed




Server wird beendet - Lösche Semaphor 53248002.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1285
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334405
  j =  1                              :        599997430
  j =  2                              :             1285
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     569
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.69
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   35.06
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.69
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.64
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  482.29
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1414.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.73
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:08.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.37
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.79
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5111.34
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:59.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908110
  j =  2                              :            45939
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45884
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869884
  j =  1                              :        399908236
  j =  2                              :            45876
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9979

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:42.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.38
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.44
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.88
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.28e-3
p-value of test                       :    0.9987

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.96
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.54
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.15
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.31
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.56
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.97
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.48
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.90
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.42
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.69
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.13
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.77
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.31
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.55
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.68
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.70
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.71e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.43e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.38
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10227.52
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.82
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4143.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11987.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11957.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.76
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  8000129076

Normal statistic for number of bits   :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.59
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000003517

Normal statistic for number of bits   :   0.028
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.28

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:40.88

 All tests were passed




Server wird beendet - Lösche Semaphor 54460418.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.66

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4222
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.59
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     887
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.98
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     667
p-value of test                       :  3.8e-3

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.07
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   33.92
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.09
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.75
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.01
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:46.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.27
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:42.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4948.83
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:02.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908404
  j =  2                              :            45795
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45674
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869674
  j =  1                              :        399908655
  j =  2                              :            45668
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.13e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.86
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.71
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.54
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.59
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17400.34
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.25
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.55
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.04
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.08
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.48
p-value of test                       :  5.7e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.48
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.43
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  539.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.12
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.36
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.00
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.53
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.59
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.86
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.56
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.22
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.30
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.10
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.74
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.38
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.84
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.32
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.70
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    2.74
p-value of test                       :  3.0e-3



-----------------------------------------------
CPU time used                    :  00:02:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.75
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10019.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9804.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.4e-4    *****

Anderson-Darling statistic = A2       :    4.84
p-value of test                       :  3.6e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5140.41
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.52
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.70
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.65
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  7999942131

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.58
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000157630

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:22.81

 All tests were passed




Server wird beendet - Lösche Semaphor 55476226.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4457
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4484
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7158
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     912
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    2.45
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     658
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.51
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.88
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.66
p-value of test                       :  6.0e-3

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  256.45
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.55
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.55
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:03:23.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:43.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4949.88
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:59.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45670
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869670
  j =  1                              :        399908661
  j =  2                              :            45668
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45921
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869921
  j =  1                              :        399908161
  j =  2                              :            45915
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:32.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.41e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.58
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.05
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.70
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.15
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.35
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17463.27
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:00:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.35
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.52
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.43
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.36
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.92
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.85
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.95
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.03
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.43
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.00
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.76
p-value of test                       :  7.6e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.02
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.24
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.67
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   97.87
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.13
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.55
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.68
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.32
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.80
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.49
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.15
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.51
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.47e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.89e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.66
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.02
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9849.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10030.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:04:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.23
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.63
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11497.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.41
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.68
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000048718

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:03.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.07
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999844763

Normal statistic for number of bits   :   -1.23
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.65
p-value of test                       :    0.05

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:20.45

 All tests were passed




Server wird beendet - Lösche Semaphor 56524802.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4217
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    2.46
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.15
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.24
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.78
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.45
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.30
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.54
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.76
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.03
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.20
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.80
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:20.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.20
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5184.42
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45908
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869908
  j =  1                              :        399908187
  j =  2                              :            45902
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907877
  j =  2                              :            46048
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:31.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.91
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.79
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.95
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.04
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   92.54
p-value of test                       :    0.9946

-----------------------------------------------
CPU time used                    :  00:00:43.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17331.49
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.37
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.31
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.31
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.02
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.77
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  103.56
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.84
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.62
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.85
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.54
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.62
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.45
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  324.87
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.21
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.00
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  325.42
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.85
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.33
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.68
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.42e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.04
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.99
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.21
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10017.48
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9958

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.99
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4916.24
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3995.47
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.91
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999969815

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.66
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999975023

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.23

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:49.06

 All tests were passed




Server wird beendet - Lösche Semaphor 57573378.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:48.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:28.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5553
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4436
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    1.72
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    3.29
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.76
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.88
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.05
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.08
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6949.02
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.71
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.49
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.28
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5072.25
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:58.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45941
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869941
  j =  1                              :        399908121
  j =  2                              :            45935
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.58e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.76e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.95
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.26
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.55
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  159.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.60
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.91
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.29
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.91
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.09
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.41
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.33
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.05
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.83
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.94
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  106.39
p-value of test                       :    0.9943


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.87
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.52
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.03
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.05
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.06
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.50
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.47
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5069.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.05
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.03
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.67
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.08
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    1.05
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.47e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.07
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.85
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10006.90
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9972.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4811.31
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.62
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.99
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11802.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.94
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000143728

Normal statistic for number of bits   :    1.14
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.24
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999890957

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.013
p-value of test                       :    0.49

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:59.95

 All tests were passed




Server wird beendet - Lösche Semaphor 58654722.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997455
  j =  2                              :             1271
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:52.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1510
p-value of test                       :  5.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334630
  j =  1                              :        599996980
  j =  2                              :             1510
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7457
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4244
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:12.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    3.90
p-value of test                       :  9.8e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.59
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:17.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.64
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.26
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.45
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.07
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1444.13
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6888.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.68
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:48.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.19
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:42.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.34
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:30.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45940
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869940
  j =  1                              :        399908122
  j =  2                              :            45936
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46259
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870259
  j =  1                              :        399907491
  j =  2                              :            46241
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 3.47e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.65e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.19
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.15
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.63
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.49
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    5.50
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   85.60
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17183.49
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.13
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.67
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.32
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.83
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.15
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.33
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.65
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.85
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.38
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.07
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.99
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.42
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4970.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.17
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.44
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.76
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.23
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.15
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.30e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 7.96e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.19
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.36
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:21.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.38
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10025.31
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10274.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.073
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4923.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5079.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.38
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11682.60
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.69
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000010966

Normal statistic for number of bits   :   0.087
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.67
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999982385

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    5.66
p-value of test                       :  1.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.53
p-value of test                       :  2.1e-4    *****

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:26.64
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           5.4e-5
 72  Savir2                          0.9991 
 104  AutoCor, d=3, r=0               2.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59703298.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:48.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9944


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9975


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9930

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.39
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.24
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:20.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.70
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1412.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:07.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.33
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4877.54
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46345
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870345
  j =  1                              :        399907311
  j =  2                              :            46343
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45760
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869760
  j =  1                              :        399908484
  j =  2                              :            45752
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:31.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.06e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.16
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.13
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.38
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.97
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17648.94
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.35
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.21
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.81
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.01
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.55
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.39
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.43
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.83
p-value of test                       :    0.9949


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.35
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.55
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.26
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.67
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.29
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.88
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  454.83
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.82
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.71
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.26
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.49
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.82
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5106.86
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.50
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.50
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.19
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    2.46
p-value of test                       :  7.0e-3



-----------------------------------------------
CPU time used                    :  00:02:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-4
p-value of test                       :    0.9971

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.55
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.85
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.80
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.75
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:57.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.0e-3

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10112.61
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.61
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4847.86
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.35
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.60
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000012949

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.49
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  8000081745

Normal statistic for number of bits   :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:38.59

 All tests were passed




Server wird beendet - Lösche Semaphor 60751874.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:09.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:10.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.75
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    4.21
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:02:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.68
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.50
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.37
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.78
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  391.22
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.82
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.68
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.64
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:07.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.79
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.20
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.92
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908448
  j =  2                              :            45773
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45857
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869857
  j =  1                              :        399908291
  j =  2                              :            45847
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.31e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 2.59e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.80
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.37
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.66
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.76
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.30
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9983

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.07
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.89
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.63
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.00
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.97
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.13
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.91
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.30
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.11
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.18
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.43
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.93
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.27
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.65
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.72
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.69
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.04
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.75
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.37
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.61
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.16
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.05
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.13
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5044.17
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.34
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.61
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.73
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.94
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.38
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.34
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : -8.13e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4650.45
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.35
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.05
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4016.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.28
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11595.74
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.97
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000134455

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.58
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000043591

Normal statistic for number of bits   :    0.34
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         : 8.98e-3
p-value of test                       :    0.50

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.87

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:36.27

 All tests were passed




Server wird beendet - Lösche Semaphor 61800450.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7427
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    3.97
p-value of test                       :  9.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.39
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.28
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  385.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.54
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.67
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.77
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5070.56
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:57.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46385
p-value of test                       :  9.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870385
  j =  1                              :        399907234
  j =  2                              :            46377
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908076
  j =  2                              :            45947
  j =  3                              :               10
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:09.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:41.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.92
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.99
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.97
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.41
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.86
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:19.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.48
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.49
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:48.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.11
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.67
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.01
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.33
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:34.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.70
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.00
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.98
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   49.73
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.45
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.01
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.55
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.33
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  188.44
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.08
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.06
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:40.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.75
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4928.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:32.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.16
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.11
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5083.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.63
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.15
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:32.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.20
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:11.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.62
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.19
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.25
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.57
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9800.93
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.55
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4792.22
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4136.13
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4162.37
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.84
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.43
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.39
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999818798

Normal statistic for number of bits   :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.14
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999925148

Normal statistic for number of bits   :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    2.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.62
p-value of test                       :    0.05

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:00:22.03

 All tests were passed




Server wird beendet - Lösche Semaphor 62849026.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.19
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.74
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  411.31
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1417.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7182.30
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.91
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.24
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.31
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:39.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.58
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46263
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870263
  j =  1                              :        399907475
  j =  2                              :            46261
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45464
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869464
  j =  1                              :        399909080
  j =  2                              :            45448
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.9998    *****

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.77e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 9.40e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.22
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.39
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.36
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    4.77
p-value of test                       :  3.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.48
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.25
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:18.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.71
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17702.65
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.14
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.86
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.87
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.45
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.04
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.27
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.47
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.73
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.00
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.32
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.45
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.16
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.01
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  317.12
p-value of test                       :    0.9945


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.72
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  326.03
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.34
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  443.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.10
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4792.48
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.90
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.56
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.63
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  : -1.49e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-3
p-value of test                       :    0.9982

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 5.51e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.48
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:13.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9959

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4338.01
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.33
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11806.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.22
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999903398

Normal statistic for number of bits   :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.24
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999985712

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.09
p-value of test                       :    0.14

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:58.23

 All tests were passed




Server wird beendet - Lösche Semaphor 42041347.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:28.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5349
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.72
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     556
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.42
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.66
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.43
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.11
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.91
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.74
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6856.82
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.09
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.40
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.69
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4969.79
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46140
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870140
  j =  1                              :        399907722
  j =  2                              :            46136
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:32.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.89
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.86
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.98
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.10
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.70
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17519.15
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.73
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.48
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.27
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.98
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.51
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.02
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.17
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  450.58
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.48
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.08
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.39
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.65
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.60
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.20
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.19
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.44
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.27
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.32
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.32
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.79
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.88
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:15.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    0.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.22e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.69e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   20.22
p-value of test                       :  9.5e-3

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:29.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.72
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10285.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.33
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.66
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.35
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4117.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.87
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.56
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.57
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999966068

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.43
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999879314

Normal statistic for number of bits   :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :  -0.030
p-value of test                       :    0.51

Sample variance                       :    0.40
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:30.51

 All tests were passed




Server wird beendet - Lösche Semaphor 43483139.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4321
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.47
p-value of test                       :  6.1e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    3.25
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.70
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.91
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.28
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.17
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.80
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.31
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.32
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.22
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4922.41
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:34.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45507
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869507
  j =  1                              :        399908989
  j =  2                              :            45501
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46151
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870151
  j =  1                              :        399907701
  j =  2                              :            46145
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:32.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.45e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.21
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:53.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.05
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.92
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.67
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.11
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.14
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.16
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.86
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.05
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.58
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.13
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.54
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.84
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.89
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.08
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  471.74
p-value of test                       :  1.5e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5014.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.06
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.81
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.19
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.43
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.00
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.02
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.81
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.04
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.76
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10186.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.043
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.48
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.33
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4254.96
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.72
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:33.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:35.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.28
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999984695

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.86
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999922574

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:13.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs NP, t = 3            6.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44531715.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:16.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    2.49
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.22
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     117
p-value of test                       :    0.9970

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.93
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.27
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.33
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  205.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.26
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1495.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7209.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.04e-3
p-value of test                       :    0.9906

Kolmogorov-Smirnov- statistic = D-    :    0.63
p-value of test                       :  9.5e-3

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   52.03
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.05
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.28
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:42.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.64
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45677
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869677
  j =  1                              :        399908647
  j =  2                              :            45675
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907970
  j =  2                              :            46009
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:31.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:10.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.92e-6
p-value of test                       :    0.9981

Kolmogorov-Smirnov- statistic = D-    : 3.19e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.90
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.11
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-3
p-value of test                       :    0.9989

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   68.62
p-value of test                       :  3.2e-3

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.12
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.73
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.89
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.64
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.75
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.90
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.90
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.83
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.50
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.60
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.05
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.12
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.43
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.59
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.76
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5058.04
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.14
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.95
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.99
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    2.58
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    2.11
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.49e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.05
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.48
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.07
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.64
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10216.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.47
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.50
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4212.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.08
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11701.73
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.00
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999941558

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.89
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999979070

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:03.96

 All tests were passed




Server wird beendet - Lösche Semaphor 45776899.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:53.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1234
p-value of test                       :    0.9998    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334354
  j =  1                              :        599997532
  j =  2                              :             1234
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5408
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:50.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4227
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.68
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:20.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.68
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.61
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.63
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6930.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.95
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.13
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5091.79
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46192
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870192
  j =  1                              :        399907619
  j =  2                              :            46186
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45637
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869637
  j =  1                              :        399908732
  j =  2                              :            45625
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.26e-6
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   98.43
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.73
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.68
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.22
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.88
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.92
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.44
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17563.88
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.70
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.56
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.80
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.87
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.82
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.61
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.40
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.97
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  409.23
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.26
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.91
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.17
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.74
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.89
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.08
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.49
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.69
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.20
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.53
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.82
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.57
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.44
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.65
p-value of test                       :    0.95

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.82
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.40
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.75
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9859.47
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9929.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.58
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.94
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11649.42
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:31.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11769.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.77
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000043669

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.93
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000097615

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:13.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9998 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47022083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:52.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4388
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7502
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4337
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7193
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.55
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.9910

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    3.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    3.70
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.85
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1440.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.95
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.89
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.43
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.48
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:14.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907665
  j =  2                              :            46166
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908686
  j =  2                              :            45654
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.50e-3
p-value of test                       :    0.9926

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.33e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.82e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.36
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.54
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.88
p-value of test                       :    0.9942

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.56
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.06
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.93
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17632.36
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.57
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.90
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.16
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.65
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.36
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.53
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.70
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.47
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.45
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  437.69
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.27
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.94
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.61
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.14
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.47
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5010.89
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.78
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.60
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.10
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.82
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.61
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.55
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.55
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 5.93e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9977

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.04
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.22
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.65
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4763.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.77
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4186.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.91
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.28
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999894752

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.21
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999898661

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    2.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:35.70

 All tests were passed




Server wird beendet - Lösche Semaphor 47939587.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:42.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    3.52
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.37
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.35
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.77
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    3.36
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.20
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.72
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.64
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  514.64
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7225.70
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.62
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.81
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5219.98
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:02:57.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45822
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869822
  j =  1                              :        399908363
  j =  2                              :            45808
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46143
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870143
  j =  1                              :        399907720
  j =  2                              :            46131
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.79e-4
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 2.11e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.41
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.11
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.48
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.00
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.60
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.10
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17145.40
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.30
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.83
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.05
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.79
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.94
p-value of test                       :    0.9936


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.71
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  408.36
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.43
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.97
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.61
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.38
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.37
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.60
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.71
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.10
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.94
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.83
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.59
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.94
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4822.86
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.22
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.78
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.39
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.59
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.34e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.34
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.48
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.11
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4146.90
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11674.19
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:32.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.93
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.28
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999863126

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.58
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999962594

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         : -4.22e-3
p-value of test                       :    0.50

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.22
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:14.45

 All tests were passed




Server wird beendet - Lösche Semaphor 48988163.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5444
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.21
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.64
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   74.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.84
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.73
p-value of test                       :    0.9902

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.73
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1529.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.44
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.12
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5088.67
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:55.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908396
  j =  2                              :            45796
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908287
  j =  2                              :            45849
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:30.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.56e-4
p-value of test                       :  2.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    : 3.29e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    6.66
p-value of test                       :  4.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.47e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.048
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.100
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.022
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.56
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.25
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   19.79
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.19e-3
p-value of test                       :    0.9912

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.75
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.9921

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.57
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17423.47
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.66
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.07
p-value of test                       :    0.9926


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.26
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.45
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.70
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.11
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.85
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.34
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.44
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.20
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.00
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.57
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.32
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.74
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.49
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.02
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.62
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.54
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.23
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.76
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.56
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.14
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.43e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 5.65e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.22
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.36
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9777.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10184.76
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.10
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.33
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.83
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000125503

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.85
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000090502

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.23
p-value of test                       :    0.99

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:33.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 53  SampleMean, r = 0               4.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49905667.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5193
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:03:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4228
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7249
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:02.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.74
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    2.66
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    3.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.11
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.47
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.24
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.67
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.18
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.68
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7176.86
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   33.22
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.28
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.81
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.56
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45972
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869972
  j =  1                              :        399908059
  j =  2                              :            45966
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.48e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 4.35e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.86
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.60
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.82
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.93
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9927

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.74
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.45
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.43
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.58
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.70
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.39
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.29
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.34
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.80
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.01
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  440.45
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.38
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.53
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.61
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.70
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.55
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.06
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.62
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.89
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.39
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.45
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 7.83e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.41
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.17
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:04:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.88
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4037.84
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.25
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.51
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000041794

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.62
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999850460

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.01
p-value of test                       :    0.02

Sample variance                       :    2.51
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.9965

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.29
p-value of test                       :    0.01

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:24.26
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50888707.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:11.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:09.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.14
p-value of test                       :    0.9993    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    5.36
p-value of test                       :  2.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     261
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.68
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.49
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.05
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.59
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7100.89
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.78
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.37
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.31
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5198.10
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908070
  j =  2                              :            45959
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46212
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870212
  j =  1                              :        399907577
  j =  2                              :            46210
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:20.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:39.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.20
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.49
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.55
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.88
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.44
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.20
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.84
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.66
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:18.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.33
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.72
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.50
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.21
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.10
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.77
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.50
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.71
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.00
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.20
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.04
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.02
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5080.41
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.64
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.18
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.74
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.60
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.17
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.62
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.56
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 4.52e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.16
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.58
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.14
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10194.62
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:34.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5103.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.11
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4288.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4421.92
p-value of test                       :  5.0e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12078.75
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11623.61
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.72
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000007459

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.21
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000073552

Normal statistic for number of bits   :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:01.34
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP1, t = 5          0.9993 
 98  HammingIndep, L=300, r=26       5.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51904515.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:42.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:12.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.69
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.77
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.17
p-value of test                       :    0.9958

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:12.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.70
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.81
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.54
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   12.24
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.56
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5220.50
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:57.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908477
  j =  2                              :            45760
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908336
  j =  2                              :            45826
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:32.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:21.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.74
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.80
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17745.63
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.21
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.79
p-value of test                       :    0.9945


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.57
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.87
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.06
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.38
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.04
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.33
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  550.92
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.93
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.84
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.77
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.81
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.10
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.33
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.20
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.99
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.40
p-value of test                       :    0.08

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.69
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.04e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.84e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.38
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.60
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.50
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5069.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4419.37
p-value of test                       :  5.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.99
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11941.20
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.64
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000097432

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.68
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000127666

Normal statistic for number of bits   :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.67
p-value of test                       :  4.4e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -3.01
p-value of test                       :    0.9987

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:06.62
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53116931.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4189
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:04:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    2.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.75
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.05
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  185.05
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  429.39
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1434.53
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.97
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.62
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.56
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.77
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.63
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.02
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:55.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46116
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870116
  j =  1                              :        399907772
  j =  2                              :            46108
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908284
  j =  2                              :            45855
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  4.9e-3

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.27e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.08e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.98
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.50
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.74
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.64
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.37
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.25
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.65
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.67
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.76
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.34
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  192.08
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.44
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.71
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.35
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.72
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.95
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.79
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.20
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.82
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.84
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.52
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.74
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.05
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.75
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -1.65
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.35
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:28.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    2.05
p-value of test                       :    0.02

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937

-----------------------------------------------
CPU time used                    :  00:00:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.22e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.15
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.23
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.72
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.89
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:14.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.95
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4085.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4179.94
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11763.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.27
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000058966

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.89
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000058249

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.96

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.62

 All tests were passed




Server wird beendet - Lösche Semaphor 54198275.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4494
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7442
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:41.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4441
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7247
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     854
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.35
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     263
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.21
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.02
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.25
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.08
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.36
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.81
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.17
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.88
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4918.96
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:13.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:00.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45821
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869821
  j =  1                              :        399908360
  j =  2                              :            45817
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908627
  j =  2                              :            45679
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 7.32e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.50e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.033
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.29
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.86
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.18
p-value of test                       :    0.9924

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.26
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.16
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.80
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.18
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17444.43
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.45
p-value of test                       :    0.9903


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.29
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.89
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.53
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.54
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.71
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.47
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.99
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.03
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.71
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.55
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.41
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.33
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.02
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.66
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.06
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.42
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.54
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4978.57
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.01
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.95
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.26
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.18
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 9.31e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.86
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.72
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.76
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.50
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9903.54
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4406.76
p-value of test                       :  8.8e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11631.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11587.94
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.25
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  7999881720

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.53
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999959072

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.45
p-value of test                       :    0.93

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:12.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       8.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55246851.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:55.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:39.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7241
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7589
p-value of test                       :  8.4e-4    *****


-----------------------------------------------
CPU time used                    :  00:04:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    3.69
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    5.04
p-value of test                       :  2.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     305
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.32
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.41
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.73
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.07
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.81
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  415.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1348.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6960.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.15
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5170.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:01.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45880
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869880
  j =  1                              :        399908242
  j =  2                              :            45876
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45947
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869947
  j =  1                              :        399908113
  j =  2                              :            45933
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :  2.7e-3

Anderson-Darling statistic = A2       :    5.30
p-value of test                       :  2.1e-3


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.05e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:40.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.57
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.66
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.46
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.34
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.73
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.78
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.69
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.83
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.79
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.04
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.32
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  498.54
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.72
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.17
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.32
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.24
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.72
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5246.76
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.76
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.30
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5144.28
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.51
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.18
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.10
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.49
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.15e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.48
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.26
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9978.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:01.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.48
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5033.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.62
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3908.86
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4022.17
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11658.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.26
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999901760

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.51
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  7999995864

Normal statistic for number of bits   :  -0.033
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   0.094
p-value of test                       :    0.46

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:35.40
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 20  BirthdaySpacings, t = 16        8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56229891.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.43
p-value of test                       :  1.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.89
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.96
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.10
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.01
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1432.40
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:07.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.91
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.34
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.44
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907944
  j =  2                              :            46025
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907735
  j =  2                              :            46128
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 3.23e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.46
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.65
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.59
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.21
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.45
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.28
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.21
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17574.48
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:55.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.63
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.17
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.80
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.80
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.60
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.79
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.19
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  170.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.43
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.68
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.23
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.02
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.21
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.56
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.12
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.15
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.72
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.16
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.33
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.68
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.78

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.29e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.71
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.67
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 8.57e-3
p-value of test                       :    0.9907

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.44
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:02.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.18
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3997.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11636.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12014.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.41
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999835856

Normal statistic for number of bits   :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.61
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000050647

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:10.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:18.62

 All tests were passed




Server wird beendet - Lösche Semaphor 57245699.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1486
p-value of test                       :  6.0e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334606
  j =  1                              :        599997028
  j =  2                              :             1486
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5399
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7501
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.42
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.49
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  502.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.47
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.63
p-value of test                       :  9.4e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.20
p-value of test                       :  7.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.10
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.87
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:08.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.97
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4880.23
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46145
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870145
  j =  1                              :        399907712
  j =  2                              :            46141
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908478
  j =  2                              :            45758
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.43e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.70e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.055
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.91
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.78
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.90
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.34
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.01
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.01
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.60
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.68
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17293.28
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.98
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.97
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.16
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.75
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.09
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.37
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.04
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.83
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.70
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.49
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.78
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.62
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.16
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.02
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.61
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  245.69
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.54
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.35
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.91
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.55
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.22
p-value of test                       :  1.0e-2


-----------------------------------------------
Normal statistic for number of jumps  :    1.38
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.61
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.21
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.46e-3
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.93
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.85
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10027.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.19
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.18
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4846.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:54.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4195.01
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.15
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999962990

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.68
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  7999990014

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.17
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :  -0.066
p-value of test                       :    0.53

Sample variance                       :    1.96
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.36
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           6.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58261507.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:41.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5481
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7480
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.84
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     611
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:18.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.25
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.12
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.05
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.40
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  479.68
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1362.06
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6893.45
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.67
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.34
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45964
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869964
  j =  1                              :        399908073
  j =  2                              :            45962
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907842
  j =  2                              :            46071
  j =  3                              :                4
  j =  4                              :                1
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:33.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :  9.4e-3

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:38.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.46e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 3.22e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.91
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 3.57e-4
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.07
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.91
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.83
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.93
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.75
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.87
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  106.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 3.48e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17843.26
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.64
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.89
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.47
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.89
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.33
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.43
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.16
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.78
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.40
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.26
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.28
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.20
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.21
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.44
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.79
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.74
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.37
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.92
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.86
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.75
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.92
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.44
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.60
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.50
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11681.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11886.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.33
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999987506

Normal statistic for number of bits   :  -0.099
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.00
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000039937

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:54.97

 All tests were passed




Server wird beendet - Lösche Semaphor 59211779.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     943
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    3.05
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    3.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    2.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.71
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     325
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.15
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.97
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7259.91
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.87
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  147.85
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.26
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908292
  j =  2                              :            45848
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45946
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869946
  j =  1                              :        399908111
  j =  2                              :            45940
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.96e-5
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.68
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.65
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17406.30
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.52
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.32
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.21
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.34
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.79
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.67
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.68
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  195.57
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.07
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.23
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.50
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.86
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.72
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.21
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.81
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.98
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5111.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.29
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.54
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.03
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.01
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.07
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.12
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.39
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.83e-3
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.77e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.54
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10183.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.55
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4342.27
p-value of test                       :  7.2e-3

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.50
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11551.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.72
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.01
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000007930

Normal statistic for number of bits   :   0.063
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.56
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  8000007537

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.98

 All tests were passed




Server wird beendet - Lösche Semaphor 60358659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:39.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997351
  j =  2                              :             1323
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     863
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.21
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     622
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    2.01
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.31
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:46.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.89
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.61
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.23
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.76
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  312.33
p-value of test                       :  3.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.77
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7127.87
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.71
p-value of test                       :  2.2e-3

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   14.87
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:07.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.80
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.89
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4966.85
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46226
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870226
  j =  1                              :        399907550
  j =  2                              :            46222
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45725
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869725
  j =  1                              :        399908553
  j =  2                              :            45719
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:31.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.6e-3

Kolmogorov-Smirnov- statistic = D-    : 9.57e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 8.29e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.14e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.85e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.35
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.27
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.93
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.34
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.22
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9907

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.37
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:28.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.14
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9935

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17476.71
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.10
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.33
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.56
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.45
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.20
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.52
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.69
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.51
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  529.49
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.88
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.35
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.99
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.87
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.85
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5159.78
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  434.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.44
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.75
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.42
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.25
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  158.19
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:35.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.44
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.12e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 8.42e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.87
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.27
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.22
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11920.98
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.50
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000249796

Normal statistic for number of bits   :    1.97
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.20
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000051907

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:09.89
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 34  Gap, r = 0                      3.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61341699.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4364
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7496
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7132
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    3.96
p-value of test                       :  9.1e-3

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.33
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.54
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.79
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.52
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.29
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.83
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1374.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.18
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.64
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5204.32
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46087
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870087
  j =  1                              :        399907829
  j =  2                              :            46081
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45709
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869709
  j =  1                              :        399908587
  j =  2                              :            45699
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920


-----------------------------------------------
CPU time used                    :  00:02:32.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.10e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.07e-5
p-value of test                       :    0.9954

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.85
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.01
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.50
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  155.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17486.54
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.01
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.78
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.82
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.67
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.30
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  546.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.45
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.39
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.41
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.35
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  461.90
p-value of test                       :  3.9e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.72
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.36
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.63
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.07
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.56
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  314.79
p-value of test                       :    0.9922


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.12
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.74
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:02:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.97
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 3.97e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.97
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.11
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.14
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.64
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9883.50
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10189.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:51.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4004.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.50
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11411.54
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.75
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.73
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000016645

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.36
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999944285

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.56

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   0.051
p-value of test                       :    0.48

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:42.01

 All tests were passed




Server wird beendet - Lösche Semaphor 62324739.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5386
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4408
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4511
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4332
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.67
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    5.59
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:02:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.97
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.13
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.91
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.70
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.27
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6807.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  148.63
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:43.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5126.85
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45459
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869459
  j =  1                              :        399909084
  j =  2                              :            45455
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907964
  j =  2                              :            46012
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.83
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.59
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.35
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.94
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:34.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.02
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.46
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.58
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.70
p-value of test                       :  9.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.21
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.49
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:34.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.83
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.85
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.52
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.08
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.41
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.09
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.70
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.65
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.27
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.32
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.65
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.03
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.70
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.46
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.42
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 6.54e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.63
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.83
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.03
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10026.46
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:28.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4841.03
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4027.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11872.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:34.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12153.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.01
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999975677

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.26
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  7999862346

Normal statistic for number of bits   :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.053
p-value of test                       :    0.48

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.04
p-value of test                       :    0.02

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.91

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:54.56

 All tests were passed




Server wird beendet - Lösche Semaphor 42074116.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5232
p-value of test                       :    0.9950


-----------------------------------------------
CPU time used                    :  00:03:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7430
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    3.27
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.08
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.31
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.47
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1354.31
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7171.06
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.03
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.53
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:48.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.80
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5004.22
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45816
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869816
  j =  1                              :        399908372
  j =  2                              :            45808
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46003
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870003
  j =  1                              :        399907995
  j =  2                              :            46001
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 4.75e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.83
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.87
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.68
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.36
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.14
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.49
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.89
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.03
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.90
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.87
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17176.19
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:55.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.71
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.26
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.34
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.74
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  464.15
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.64
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.80
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.14
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.44
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.91
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  445.93
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.62
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  156.49
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.37
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.54
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.59
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.82
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.59
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.55
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 5.59e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.79e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.22
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.97
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10081.36
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:12.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:04:32.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5031.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4924.85
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4135.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4008.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11958.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.02
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.30
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000087778

Normal statistic for number of bits   :    0.69
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.71
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999933776

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.71

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.19
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    2.44
p-value of test                       :  7.4e-3

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.82

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:12.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 54  SampleMean, r = 10              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43941919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.84
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.65
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.97
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.52
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.13
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.61
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1424.35
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7190.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.30
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.78
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.80
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:37.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.29
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46046
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870046
  j =  1                              :        399907915
  j =  2                              :            46032
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46217
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870217
  j =  1                              :        399907573
  j =  2                              :            46203
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :  7.6e-4    *****

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.0e-3


-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.37e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.97e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.71
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.19
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.97
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.13
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.99
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17019.61
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.95
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.77
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.12
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.94
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.71
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.60
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.71
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.96
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.78
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.27
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.93
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.82
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.87
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.01
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.23
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.57
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.06
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.55
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.50
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.90
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.83
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.61
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.25e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.07e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:00:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 6.48e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.43
p-value of test                       :    0.9938

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.13
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.14
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.06
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3985.84
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.82
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11766.10
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.24
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999892916

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.61
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000057868

Normal statistic for number of bits   :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:54.20

 All tests were passed




Server wird beendet - Lösche Semaphor 44924959.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:20.41

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:50.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.04
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.04
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.42
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     272
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.41
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.02
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.21
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.31
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1286.77
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7243.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.76
p-value of test                       :  8.1e-4    *****

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.6e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   49.26
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.16
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.17
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.77
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:02.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45977
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869977
  j =  1                              :        399908051
  j =  2                              :            45967
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.98

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46213
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870213
  j =  1                              :        399907577
  j =  2                              :            46207
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:29.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.07e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.35e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.10
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.42
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  105.90
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    : 8.40e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17672.71
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.24
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.56
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.65
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.11
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.40
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.96
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.87
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.17
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.59
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.62
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.70
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.19
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5030.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.09
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.26
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.11
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.95
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.62
p-value of test                       :  4.5e-3


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.05
p-value of test                       :    0.85

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.42e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.43
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.67
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.08
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10156.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10042.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:02.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.090
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4789.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.07
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4078.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.76
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11904.69
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:32.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11852.89
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.00
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999989312

Normal statistic for number of bits   :  -0.084
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.56
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999857501

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.38

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :  -0.093
p-value of test                       :    0.54

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.44
p-value of test                       :    0.67

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:03.29

 All tests were passed




Server wird beendet - Lösche Semaphor 45809695.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:39.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     635
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    6.39
p-value of test                       :  7.3e-4    *****


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.48
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.42
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.70
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.57
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.93
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  490.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1493.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6873.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:52.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.61
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.69
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.86
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:00.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45936
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869936
  j =  1                              :        399908134
  j =  2                              :            45924
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45930
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869930
  j =  1                              :        399908147
  j =  2                              :            45916
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.14e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.36
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.57
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.40
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.78
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  113.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :  8.9e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17036.13
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.00
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.51
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.34
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.70
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.95
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.17
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.23
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.43
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.15
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.23
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.21
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.96
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.40
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.93
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.29
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  336.60
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.33
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.78
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.92
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.32e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.40
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.9934

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.92
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10099.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9950.91
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4809.29
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5126.30
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4202.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.43
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12244.11
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.56
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.81
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999859892

Normal statistic for number of bits   :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.05
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  7999946523

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:30.87
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs NP, t = 16           7.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46759967.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:42.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:53.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5545
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     949
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.93
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.74
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.52
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.76
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.22
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.31
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.44
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.76
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.35
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.06
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7095.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:08.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.59
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.85
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:30.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46184
p-value of test                       :    0.08


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870184
  j =  1                              :        399907635
  j =  2                              :            46178
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46005
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870005
  j =  1                              :        399907993
  j =  2                              :            45999
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:48.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.02e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.47
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.24
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.11
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.45
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17503.71
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.51
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.22
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.52
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.36
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.47
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.72
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.26
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.69
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.24
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.88
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.73
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.84
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.59
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.67
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4827.56
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.21
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.45
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.68
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.59
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4887.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.61
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.77
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.04
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    0.61
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.84
p-value of test                       :    0.9966


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.77e-3
p-value of test                       :    0.9939

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.00e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.33
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.04
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.12
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9788.99
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.96
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4126.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11727.70
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.27
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000214711

Normal statistic for number of bits   :    1.70
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.88
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000191740

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.41
p-value of test                       :    0.08

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:44.34

 All tests were passed




Server wird beendet - Lösche Semaphor 47710239.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:52.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.86
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:12.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9971

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:41.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.52
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.20
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.88
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  443.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1515.90
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.85
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.82
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.89
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.06
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45937
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869937
  j =  1                              :        399908128
  j =  2                              :            45933
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46131
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870131
  j =  1                              :        399907743
  j =  2                              :            46121
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.57e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:40.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.67
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.56
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.82
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.37
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:40.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17610.06
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:00:55.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.37
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.37
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.15
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.59
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.64
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.72
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.35
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.75
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.11
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.55
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.15
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.08
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.76
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.18
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.49
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.20
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5137.59
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.59
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.67
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.61
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.39
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.28
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.93
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.81
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.01
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.71

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.56e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.71e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.50
p-value of test                       :    0.9927

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.10
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  260.33
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:02:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9802.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10240.93
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4743.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.23
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:54.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11667.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.64
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000063772

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.98
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999891296

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:13.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.31
p-value of test                       :    0.38

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:24.21

 All tests were passed




Server wird beendet - Lösche Semaphor 48758815.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1512
p-value of test                       :  4.4e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334632
  j =  1                              :        599996976
  j =  2                              :             1512
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4236
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:40.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     938
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.97
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     568
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.33
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.15
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.52
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.00
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7096.33
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.02
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:08.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.05
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.41
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.84
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:57.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45872
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869872
  j =  1                              :        399908258
  j =  2                              :            45868
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908430
  j =  2                              :            45782
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9905

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.57e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.53e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.73
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.64
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.49
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.84
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.46
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.32
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.14
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17622.57
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.60
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.84
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.79
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.44
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.12
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.95
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.76
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.53
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.88
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.07
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.76
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.52
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.27
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.97
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.72
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.17
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.40
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.49
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.55
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.67
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.29
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.99
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.10
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.38
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.37
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -0.40
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 8.07e-3
p-value of test                       :    0.9913

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.35
p-value of test                       :    0.91

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.51e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 9.74e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.03
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.87
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9737.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:20.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.42
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4987.67
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.46
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.59
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12169.12
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11942.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.99
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999825410

Normal statistic for number of bits   :   -1.38
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.58
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000048844

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   0.078
p-value of test                       :    0.47

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           4.4e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49709087.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5382
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.28
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.73
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.95
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     130
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.87
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.30
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.29
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.21
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1546.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6943.97
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.11
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.28
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.81
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.49
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4842.20
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:03.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908520
  j =  2                              :            45731
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907707
  j =  2                              :            46142
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.6e-3

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 4.12e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.37e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.60
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.84
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.84
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.12
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.15
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.81
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17429.74
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   58.32
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.57
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.79
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.86
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.67
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.06
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.09
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.86
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  449.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.36
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.12
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.19
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.75
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.97
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  173.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.95
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.10
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.73
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.14
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.81
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.93
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.11
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.90
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.91
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    3.10
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.03
p-value of test                       :    0.98

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.37e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 5.30e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.18
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.18
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.41
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9818.84
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9771.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4694.89
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4856.65
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4220.02
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11699.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.38
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.71
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999864332

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   82.86
p-value of test                       :  7.0e-3


-----------------------------------------------
Total number of bits:  7999955520

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:54.18

 All tests were passed




Server wird beendet - Lösche Semaphor 50692127.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:50.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9925


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.18
p-value of test                       :    0.9950

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.38
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.76
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.37
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.35
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.03
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.61
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.44
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6915.64
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.45
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4967.90
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45881
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869881
  j =  1                              :        399908242
  j =  2                              :            45873
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46072
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870072
  j =  1                              :        399907862
  j =  2                              :            46060
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:33.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.92
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.47
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.88
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.01
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.29
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.23
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.46
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.73
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.62
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.12
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.09
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.04
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.91
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.07
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.13
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.83
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.23
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.29
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.69
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.00
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.29
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.04
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.38
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.91
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.75
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.35
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.38
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9914.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10031.31
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.69
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4045.44
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12110.15
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12020.09
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.04
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000160522

Normal statistic for number of bits   :    1.27
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.80
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999904787

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:31.15

 All tests were passed




Server wird beendet - Lösche Semaphor 51740703.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5354
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:42.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     271
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.85
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.99
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   29.10
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.72
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  258.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  402.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1449.86
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6972.35
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.13
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  141.94
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4984.06
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:01.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907841
  j =  2                              :            46072
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907703
  j =  2                              :            46144
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.29e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.52e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.55e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.73
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.56
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.62
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.24
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.91
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.59e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.37
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.15
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.47
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.71
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.18
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.56
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.47
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.49
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.30
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.35
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.60
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.62
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.62
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.12
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.10
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.70
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.99
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.23
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    2.26
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.75
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.81e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.05e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.73
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.16
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.53
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.65
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.84
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.04
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.77
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4920.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.87
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:31.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.38
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.79
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  8000057427

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.43
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999982295

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:54.27

 All tests were passed




Server wird beendet - Lösche Semaphor 52822047.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1307
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334427
  j =  1                              :        599997386
  j =  2                              :             1307
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5316
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    2.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     328
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.95
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    2.78
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.26
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.06
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   77.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:08.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.17
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.57
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4952.78
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45860
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869860
  j =  1                              :        399908286
  j =  2                              :            45848
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45810
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869810
  j =  1                              :        399908387
  j =  2                              :            45796
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.30e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.41e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.57e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.6e-3

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.44
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.81
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.77
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.32
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.068
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.09
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17604.16
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.11
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.30
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.84
p-value of test                       :  8.8e-3


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.49
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.68
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.97
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  190.51
p-value of test                       :  7.8e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.04
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.09
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.25
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.60
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.94
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.74
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.68
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.80
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.52
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.99
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.16
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.03
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    1.51
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.56
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.43e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 4.13e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.70
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.63
p-value of test                       :    0.9903

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.62
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9923.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -2.99e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4927.57
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4749.59
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4123.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.90
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11938.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11729.09
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.05
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999978413

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999895760

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  4.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.16
p-value of test                       :    0.98

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.61

 All tests were passed




Server wird beendet - Lösche Semaphor 53837855.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1450
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334570
  j =  1                              :        599997100
  j =  2                              :             1450
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4308
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7390
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.22
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     566
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.16
p-value of test                       :    0.9976

Stat. AD after spacings (mNP2-S)      :    2.16
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9955

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9923

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     127
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.66
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.49
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.01
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.66
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.71
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.42
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.14
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1360.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6902.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.80
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.80
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   93.05
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.52
p-value of test                       :    0.9913


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   85.49
p-value of test                       :    0.9912


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4968.51
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45615
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869615
  j =  1                              :        399908772
  j =  2                              :            45611
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907911
  j =  2                              :            46037
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:31.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.26e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.59e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.34
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.67
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.83
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.26
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.29
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.22
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  110.58
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:40.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17619.43
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.63
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.40
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.97
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.81
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.30
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.88
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.65
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  471.14
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.38
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.18
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.53
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   96.49
p-value of test                       :    0.9958


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.91
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.21
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.23
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.11
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.80
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.88
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4932.24
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.90
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.94
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.29
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  : 2.98e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 2.91e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.29
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.86
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10222.26
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5014.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11822.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11583.35
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.43
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999971039

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.96
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000036616

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.52
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.069
p-value of test                       :    0.47

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:49.20

 All tests were passed




Server wird beendet - Lösche Semaphor 54853663.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:40.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7414
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4264
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:59.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.11
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.41
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    4.40
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:02:12.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.52
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.84
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.77
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.40
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1400.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7114.72
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.19
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.86
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  111.38
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.73
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908236
  j =  2                              :            45870
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46020
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870020
  j =  1                              :        399907963
  j =  2                              :            46014
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:30.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.79e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.10
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.18
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.09
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.65
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.72
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.52
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.12
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  148.86
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17390.84
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.64
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.60
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.66
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.60
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.88
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.50
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.84
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.31
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.37
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.40
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.61
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.29
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.30
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.91
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.88
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.46
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.23
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.55
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.98
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  432.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.38
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.65
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.76
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.94
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    0.72
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.35
p-value of test                       :    0.9906

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.97e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.49e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.96
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.94
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.26
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:09.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9975.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:04:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4798.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.59
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4112.46
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.13
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.41
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999929276

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.60
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000000292

Normal statistic for number of bits   : 2.31e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.97

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:57.38

 All tests were passed




Server wird beendet - Lösche Semaphor 55869471.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:40.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:42.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:11.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:10.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.00
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     589
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     315
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:42.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.14
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:10.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.61
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.38
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.05
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:30.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  434.60
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.31
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.13
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.25
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4961.70
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:01.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45991
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869991
  j =  1                              :        399908022
  j =  2                              :            45983
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45738
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869738
  j =  1                              :        399908524
  j =  2                              :            45738
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 4.70e-3
p-value of test                       :    0.9944

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.07e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.81e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.84e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.18
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.04
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.08
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.60
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.12
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.41
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.85
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.55
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.62
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.20
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.25
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.95
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.00
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.11
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.35
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.47
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.74
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  327.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4918.05
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.26
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.54
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.13
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.53
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.65
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.64
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    1.71
p-value of test                       :    0.9997    *****


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.60
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 5.57e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.33e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 2.46e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.32
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10178.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.069
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:51.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4084.45
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.08
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.33
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.42
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000036649

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.15
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000000466

Normal statistic for number of bits   : 3.68e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:19.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 9.84e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -2.14
p-value of test                       :    0.98

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:07.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 80  LinearComp, r = 0               0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56852511.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:02:13.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:12.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.30
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    2.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    4.27
p-value of test                       :  6.5e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     331
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.47
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.63
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.84
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.36
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.38
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.49
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 6.94e-3
p-value of test                       :    0.9926

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.22
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.60
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.84
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.67
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45877
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869877
  j =  1                              :        399908248
  j =  2                              :            45873
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45888
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869888
  j =  1                              :        399908227
  j =  2                              :            45882
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:39.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.90e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.66e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.09e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  101.40
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.05
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.21
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.06
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.52
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.66
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17496.83
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.26
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.96
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.56
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.79
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.59
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.11
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.28
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.58
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.81
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.24
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.42
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.97
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.71
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.61
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.56
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.00
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.77
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.36
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.96
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5039.88
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  340.61
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.95
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.36
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.79
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.32e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.52
p-value of test                       :    0.9924

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.36
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.98
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.20
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9987.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4812.29
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4783.18
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3948.02
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4023.87
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12217.78
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:33.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11532.49
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.83
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000097312

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.18
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999933029

Normal statistic for number of bits   :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.85
p-value of test                       :    0.80

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:59.11

 All tests were passed




Server wird beendet - Lösche Semaphor 57999391.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1473
p-value of test                       :  1.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334593
  j =  1                              :        599997054
  j =  2                              :             1473
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5347
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4454
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7063
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4487
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     860
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.61
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.36
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:14.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.29
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.19
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.19
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.63
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.40
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  398.13
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1441.21
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7179.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.00
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:03:07.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.46
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5135.16
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:13.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45796
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869796
  j =  1                              :        399908412
  j =  2                              :            45788
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908379
  j =  2                              :            45809
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:42.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.93
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.43
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.53
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.50
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.37
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17166.34
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.54
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.98
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.95
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.03
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.50
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.61
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.12
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.81
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.59
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.96
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.27
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.91
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   52.49
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.78
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.54
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.05
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.70
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.21
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.76
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.54
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.52
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.26e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 2.48e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.23
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.15
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.25
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.81
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9919.65
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4983.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.83
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.78
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.65
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.44
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.23
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.25
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999837893

Normal statistic for number of bits   :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.58
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  7999997694

Normal statistic for number of bits   :  -0.018
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.45

 All tests were passed




Server wird beendet - Lösche Semaphor 59342879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5425
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    3.43
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.49
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.09
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.12
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.46
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.25
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.37
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.71
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  176.77
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  404.12
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1568.32
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:19.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.64
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5080.92
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46061
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870061
  j =  1                              :        399907885
  j =  2                              :            46047
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.53
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.67
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.20
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.59
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:28.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   11.42
p-value of test                       :  3.3e-3

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.46
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17581.14
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.81
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.75
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.81
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.10
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.01
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.01
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.59
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.21
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.87
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.53
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.06
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5172.90
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.38
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.68
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.97
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.73
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.05
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.72
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.59
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :  -0.019
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.25
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10230.35
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.95
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4832.10
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4280.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4034.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11570.31
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.13
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000074170

Normal statistic for number of bits   :    0.59
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.85
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000045613

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.71
p-value of test                       :    0.76

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:43.69

 All tests were passed




Server wird beendet - Lösche Semaphor 60260383.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:41.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4301
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7294
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7243
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:20.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     176
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9949

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:47.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.25
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.17
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.99
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.57
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  286.63
p-value of test                       :  8.4e-3

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1416.95
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7073.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.37
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.16
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:15.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.61
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4908.98
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908253
  j =  2                              :            45869
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908216
  j =  2                              :            45889
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:32.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.09e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:20.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.83e-4
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.95
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.06
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.38
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.30
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  3.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17062.61
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.06
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.28
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.43
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.32
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.09
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.70
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.51
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.85
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.13
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  178.87
p-value of test                       :  8.0e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.16
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.26
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.44
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.36
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.33
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.53
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.17
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.9e-3

Anderson-Darling statistic = A2       :    4.06
p-value of test                       :  8.5e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.63
p-value of test                       :  4.3e-3

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.91e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 8.94e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.16
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.76
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.54
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10172.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:04:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4909.25
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4059.83
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.75
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11841.65
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.78
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999932015

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.39
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000043750

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.30
p-value of test                       :    0.10

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:38.87

 All tests were passed




Server wird beendet - Lösche Semaphor 61407263.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5508
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:42.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     920
p-value of test                       :    0.26

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     606
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     282
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.39
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.91
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  496.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.64
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6901.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.00
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.01
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.46
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.23
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5045.52
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:00.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45716
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869716
  j =  1                              :        399908571
  j =  2                              :            45710
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908017
  j =  2                              :            45990
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.18
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.18
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.42
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.57
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.56
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   50.39
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:46.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17650.27
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.66
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.41
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.07
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.52
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.99
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.18
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  556.43
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.34
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.97
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.20
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.97
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.21
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.80
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.14
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.56
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  233.72
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.35
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.11
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.33
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.93
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.89
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.71
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.16
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    2.22
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.56e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.00e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.30
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.61
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9812.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10151.24
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5067.88
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.45
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12095.16
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11653.77
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.57
p-value of test                       :  4.9e-3


-----------------------------------------------
Total number of bits:  8000067210

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:59.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.57
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000103726

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:17.82

 All tests were passed




Server wird beendet - Lösche Semaphor 62455839.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7201
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:02.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.71
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:52.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     275
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:11.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:33.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.26
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.01
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.24
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.48
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6853.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.64
p-value of test                       :  8.7e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.82
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.74
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5037.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908043
  j =  2                              :            45974
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45755
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869755
  j =  1                              :        399908492
  j =  2                              :            45751
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.12
p-value of test                       :    0.9998    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.97
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.84
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.87
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.17
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.14
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17404.15
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.25
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.95
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.77
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.90
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.64
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.98
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.46
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.35
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.62
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.57
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.35
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.77
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.02
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.51
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:48.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.51
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.73
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4912.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.83
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.89
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.21
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.04
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.41
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.98
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.48
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:13.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.51
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :    1.19
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:14.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 3.87e-3
p-value of test                       :    0.9960

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.42
p-value of test                       :    0.92

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.05e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.63
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.66
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.38
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9892.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.54
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5125.07
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:52.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.12
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4403.36
p-value of test                       :  9.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.17
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11870.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.73
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.38
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000145492

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.14
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999963656

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    3.02
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    2.44
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.62
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:32.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 97  HammingIndep, L=300, r=0        9.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42106885.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1281
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334401
  j =  1                              :        599997438
  j =  2                              :             1281
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:11.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.93
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.17
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.91
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.62
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  405.50
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.21
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7032.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.59
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:09.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.00
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.74
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5118.35
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:18.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46157
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870157
  j =  1                              :        399907688
  j =  2                              :            46153
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46062
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870062
  j =  1                              :        399907881
  j =  2                              :            46052
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:30.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.35e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.20e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.74
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.63
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.18
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:41.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17529.23
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.97
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.08
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.37
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.89
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.48
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.03
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.76
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.21
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.49
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.07
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.97
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.62
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.50
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.49
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.45
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.25
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5097.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.87
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.59
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:34.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.48
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:15.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.93
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.84
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.31
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10077.02
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.94
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11912.41
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12015.44
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.94
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  7999971213

Normal statistic for number of bits   :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.29
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999935267

Normal statistic for number of bits   :   -0.51
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.75
p-value of test                       :    0.77

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:53.97

 All tests were passed




Server wird beendet - Lösche Semaphor 43515909.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5417
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     910
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:11.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.88
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.34
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.02
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.62
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:17.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:17.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   10.03
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.05
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:00.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45531
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869531
  j =  1                              :        399908942
  j =  2                              :            45523
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46194
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870194
  j =  1                              :        399907613
  j =  2                              :            46192
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    4.68
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  1.6e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:33.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:51.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.10e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.34e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.31
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.92
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.73
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17488.58
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.60
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.10
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.71
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.91
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.09
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  567.17
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.18
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.76
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.85
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.22
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.62
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.69
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.50
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.16
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.04
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.72
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.96
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.11
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.34
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.26
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 8.72e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.86
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.58
p-value of test                       :    0.9913

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.70
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10050.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4937.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.19
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4032.34
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11789.54
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.61
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  8000094294

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.61
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  7999926273

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   0.059
p-value of test                       :    0.48

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.23
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:29.45

 All tests were passed




Server wird beendet - Lösche Semaphor 44630021.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:42.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:48.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4256
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7326
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     902
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.74
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.05
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    3.13
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.65
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    2.56
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     174
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:41.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.42
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.73
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.04
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.68
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.07
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7042.52
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.62
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.44
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:38.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5063.29
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907925
  j =  2                              :            46030
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908205
  j =  2                              :            45887
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       : 1 -  9.1e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    4.03
p-value of test                       :  8.5e-3


-----------------------------------------------
CPU time used                    :  00:02:31.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.51
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.98
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.77
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   10.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.49
p-value of test                       :  5.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   97.46
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17292.80
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.38
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.65
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.52
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.96
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.49
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.72
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.86
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.96
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  565.44
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.77
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.19
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.94
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.29
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.55
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.67
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.64
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.73
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.63
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.72
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.48
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.28
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:27.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.71
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.38e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.95e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.26
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.68
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  235.87
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.98e-3
p-value of test                       :    0.9959

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.95
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10138.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:20.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4913.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.79
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.52
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.25
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11967.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11916.08
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.24
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000094351

Normal statistic for number of bits   :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.95
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999911936

Normal statistic for number of bits   :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.65
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:18.79

 All tests were passed




Server wird beendet - Lösche Semaphor 45580293.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:42.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:50.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.85
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     632
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.19
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.70
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.28
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.05
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  221.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.41
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.00
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:03:09.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.05
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4999.30
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:14.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45707
p-value of test                       :    0.79


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869707
  j =  1                              :        399908588
  j =  2                              :            45703
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:31.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.41e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.71e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.74
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.45
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.26
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.39
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  153.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17659.19
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.30
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.77
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.57
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.50
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.14
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.54
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.09
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.13
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.77
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.21
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.58
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.40
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.29
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.35
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  162.02
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  425.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  450.38
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.37
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.06
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.77
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.67
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.74
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    1.11
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:02:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.55e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 5.78e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.40e-3
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.31
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.85
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.76
p-value of test                       :  9.6e-3

-----------------------------------------------
CPU time used                    :  00:02:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.51
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.53
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4825.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.99
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4147.78
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.46
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11746.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:32.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.59
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999899096

Normal statistic for number of bits   :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.08
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999998126

Normal statistic for number of bits   :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.063
p-value of test                       :    0.47

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.90
p-value of test                       :    0.03

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:24.63

 All tests were passed




Server wird beendet - Lösche Semaphor 46596101.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:41.65

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:40.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4323
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7416
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:56.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.64
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.86
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.74
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.68
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.93
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  366.17
p-value of test                       :    0.9921

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.18
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7011.35
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.52
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   39.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.65
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.70
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5131.62
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:57.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45733
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869733
  j =  1                              :        399908536
  j =  2                              :            45729
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908062
  j =  2                              :            45963
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.85e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 5.51e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.26
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.94
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.06
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.32
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.59
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17218.93
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:00:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   50.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.23
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.80
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.31
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.42
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.21
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.40
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.35
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.35
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  109.83
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.69
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.73
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.92
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.72
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.85
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4896.22
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.28
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.05
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.41
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.27
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4938.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.54
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.91
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.76
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    2.26
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.78
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.31e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.67e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 6.78e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.84
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.94
p-value of test                       :  3.2e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  149.89
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:02:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9983.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.49
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:04:20.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4826.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4005.43
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.73
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.61
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.51
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.24
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000022339

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.24
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000024670

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    3.70
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    3.34
p-value of test                       :  4.3e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:14.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:52.85

 All tests were passed




Server wird beendet - Lösche Semaphor 47579141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:40.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7204
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:42.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.39
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.69
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.70
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.92
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.55
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.06
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.92
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1336.45
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7043.86
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.50
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.58
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.50
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.94
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4931.21
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:55.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45887
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869887
  j =  1                              :        399908229
  j =  2                              :            45881
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45839
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869839
  j =  1                              :        399908322
  j =  2                              :            45839
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:49.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.33e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.48
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.14
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.13
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.24
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.41
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.65
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.57
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.48
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.57
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.13
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.33
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.04
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.37
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.65
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.98
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.78
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.12
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.64
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   46.11
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.02
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.76
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  165.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.15
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  326.28
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.57
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5062.63
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.33
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.97
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.51
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.95
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5246.58
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.69
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.56
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.45
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.27
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.31e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.56e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.39
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.77
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9730.28
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.41
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.091
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4739.34
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:55.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.83
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000142732

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.95
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999867980

Normal statistic for number of bits   :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:10.40

 All tests were passed




Server wird beendet - Lösche Semaphor 48496645.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:49.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5464
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:02.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:12.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.47
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.81
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.71
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  505.31
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1342.13
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7089.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:08.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.41
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5108.24
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:56.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908425
  j =  2                              :            45777
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45726
p-value of test                       :    0.76


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869726
  j =  1                              :        399908550
  j =  2                              :            45722
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:48.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 3.02e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 9.61e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.081
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.64
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.30
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.24
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.65
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.03
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17369.77
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.97
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.05
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.12
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.22
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.23
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.25
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.62
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.45
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.80
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.00
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.59
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.29
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  480.27
p-value of test                       :  5.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.55
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  334.92
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.36
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.92
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.48
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5158.08
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.13
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.66
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.47
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    2.93
p-value of test                       :  1.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 5.21e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.82
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.20
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.52
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 5.61e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    3.68
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  151.80
p-value of test                       :    0.9954

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9956.83
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9807.88
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.35
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.08
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11706.33
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:34.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.82
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999896003

Normal statistic for number of bits   :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.34
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000192742

Normal statistic for number of bits   :    1.52
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-3
p-value of test                       :    0.9941

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.99
p-value of test                       :    0.02

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:44.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 78  RandomWalk1 H (L=10000, r=0)    5.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49512453.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5268
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7259
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    6.48
p-value of test                       :  5.9e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:41.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.89
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.32
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1311.70
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7097.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.94
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.21
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:03:23.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.40
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4997.76
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:56.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45566
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869566
  j =  1                              :        399908870
  j =  2                              :            45562
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46147
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870147
  j =  1                              :        399907707
  j =  2                              :            46145
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:32.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 7.89e-3
p-value of test                       :    0.9908

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.27e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.16e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   89.33
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.32
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.60
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9901

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.88
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.9964

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.49
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17501.41
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.57
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.01
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.31
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.36
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.22
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.84
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.16
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.51
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.00
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.43
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.02
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.58
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.18
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.50
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  324.23
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.51
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.50
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  349.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4826.67
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  349.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.51
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.58
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.57e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.81
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.49
p-value of test                       :    0.9929

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.56
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10179.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10053.89
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.60
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4976.70
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.79
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.52
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11831.00
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11742.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.51
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999867074

Normal statistic for number of bits   :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.37
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999864131

Normal statistic for number of bits   :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.79
p-value of test                       :    0.22

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:21.67
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 23  ClosePairs mNP2S, t = 5         5.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50495493.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1292
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334412
  j =  1                              :        599997416
  j =  2                              :             1292
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5287
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4426
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7371
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    3.55
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.09
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.48
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  267.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7115.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.57
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.42
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.64
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:00.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908170
  j =  2                              :            45909
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908068
  j =  2                              :            45963
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  9.7e-3

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:30.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:49.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.04e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 5.70e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.74
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.41
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.77
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.96
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.87
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.60
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.66
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17382.28
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.65
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.88
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.45
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.84
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.11
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.76
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.44
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.30
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.20
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.44
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.05
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.35
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.67
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.50
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.25
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5099.67
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.22
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.94
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.94
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4773.25
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.72
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.11
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.96
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :  -0.091
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.25
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.93e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.60e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.67
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.11
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.87
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.48
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10094.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.90
p-value of test                       :  1.9e-3

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4888.48
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4031.25
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.88
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11903.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.59
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999963758

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.98
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999743033

Normal statistic for number of bits   :   -2.03
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:11.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.52

 All tests were passed




Server wird beendet - Lösche Semaphor 51576837.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.56

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4466
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:11.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:04:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9928

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.20
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.99
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.26
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.54
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.23
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.59
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.22
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:19.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.30
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  131.12
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5017.04
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:57.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45829
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869829
  j =  1                              :        399908344
  j =  2                              :            45825
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45689
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869689
  j =  1                              :        399908626
  j =  2                              :            45681
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:32.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.2e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    3.72
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.96e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.47e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.71e-4
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 8.62e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.024
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.038
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.07
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.89
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.40
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.16
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.79
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.35
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.49
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.54
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.00
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.01
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.32
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.36
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.87
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.67
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.70
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.14
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.38
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.66
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5167.40
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.09
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.88
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.38
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5141.64
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.10
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.54
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.40
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.11e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.23e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.61
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.10
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.79
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.54
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:04:31.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4994.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.10
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.79
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11830.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:35.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.12
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999984899

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.97
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999961814

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.12
p-value of test                       :    0.87

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:03.43

 All tests were passed




Server wird beendet - Lösche Semaphor 52625413.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5466
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7495
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7467
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7438
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.06
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    2.40
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.82
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.49
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.35
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1478.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.07
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.51
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.77
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:32.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.87
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.37
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5116.89
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907912
  j =  2                              :            46035
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45587
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869587
  j =  1                              :        399908831
  j =  2                              :            45577
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:30.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.71e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.74e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.31
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.81
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.42
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.02
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.52
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.79
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.48
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17393.50
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.83
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.16
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.69
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.30
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.50
p-value of test                       :    0.9902


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.52
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.72
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.83
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.12
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.43
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  435.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  163.96
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.46
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.24
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.27
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4935.65
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  332.46
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.56
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.48
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.86
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.06
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.46
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.35
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 4.56e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 3.83e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.07
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.79
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  240.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.67
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10250.56
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4939.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4998.34
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.56
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.10
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11685.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.97
p-value of test                       :    0.44


-----------------------------------------------
Total number of bits:  7999982283

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.06
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999946106

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.22
p-value of test                       :    0.9917

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    3.29
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.13
p-value of test                       :    0.9989

-----------------------------------------------
CPU time used                    :  00:01:15.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:23.25

 All tests were passed




Server wird beendet - Lösche Semaphor 53739525.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5449
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7064
p-value of test                       :    0.9986


-----------------------------------------------
CPU time used                    :  00:03:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.01
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.68
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.59
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.84
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.25
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.97
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.01
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.05
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.21
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.85
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   18.66
p-value of test                       :  2.2e-3


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.63
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:00.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46034
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870034
  j =  1                              :        399907936
  j =  2                              :            46026
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45530
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869530
  j =  1                              :        399908943
  j =  2                              :            45524
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.28e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9943


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 2.07e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.17
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.46
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.80
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.40
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:52.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.53
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.34
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.22
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.54
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.02
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.81
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.70
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.32
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.12
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.11
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.05
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.50
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.93
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.38
p-value of test                       :    0.9937


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.87
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.94
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.44
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5087.57
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.48
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.46
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.99
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9946

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.47
p-value of test                       :    0.68

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 6.16e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.46e-3
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.73
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.87
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.29
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.58
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10005.19
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10154.19
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5008.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5012.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4159.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.21
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11560.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.48
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999812144

Normal statistic for number of bits   :   -1.49
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.89
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  7999926246

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.25

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.36
p-value of test                       :    0.09

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.79
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    0.63
p-value of test                       :    0.26

Sample variance                       :    2.68
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:14.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:00.61

 All tests were passed




Server wird beendet - Lösche Semaphor 54755333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7447
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4126
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     926
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.96
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    2.14
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     266
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:42.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.04
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.33
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.07
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.96
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.62
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.25
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:48.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6978.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.55
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.82
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   11.98
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.06
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5195.71
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:54.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45638
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869638
  j =  1                              :        399908727
  j =  2                              :            45632
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :  2.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    5.24
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 7.40e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.013
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.046
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.64
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   88.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.84
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.29
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.84
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.59
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17413.36
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.21
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.70
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.39
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.52
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.33
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.15
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.73
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.00
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.78
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.50
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.88
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.56
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.36
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.97
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.09
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.88
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4874.89
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.72
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.59
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.07
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.38
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.92
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.98
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.97
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.91
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.18
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.70
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.62

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.42e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.17
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.43
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.23
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.56
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:20.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.21
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4304.80
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4001.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11731.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.42
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.65
p-value of test                       :    0.68


-----------------------------------------------
Total number of bits:  8000055459

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.26
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999833879

Normal statistic for number of bits   :   -1.31
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.06
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 17  BirthdaySpacings, t = 7         0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55738373.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:40.77

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5491
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:09.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.55
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.82
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.27
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.34
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.77
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:28.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.18
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.71
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.09
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:03:18.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.73
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.97
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5082.84
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:55.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908267
  j =  2                              :            45862
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45459
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869459
  j =  1                              :        399909084
  j =  2                              :            45455
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:31.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.9910

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.52e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 2.62e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.99
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.97
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.03
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17278.72
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.00
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.12
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.66
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.66
p-value of test                       :  6.9e-3


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.70
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.78
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  569.19
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.91
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.07
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.84
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.24
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.65
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.86
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.13
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.42
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.33
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.65
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.88
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  225.24
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.93
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    1.44
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.47
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.48e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.07
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.77
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.03
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.47
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.58
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4975.52
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.87
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11847.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11925.18
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.88
p-value of test                       :    0.40


-----------------------------------------------
Total number of bits:  7999883877

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999927371

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :  -0.016
p-value of test                       :    0.51

Sample variance                       :    0.22
p-value of test                       :    0.9922

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :  -0.045
p-value of test                       :    0.52

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:39.23

 All tests were passed




Server wird beendet - Lösche Semaphor 56754181.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.22
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.90
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     166
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.26
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.67
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.84
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.11
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.80
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.87
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.42
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1548.85
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7126.98
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.82
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.13
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4960.31
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:00.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45765
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869765
  j =  1                              :        399908474
  j =  2                              :            45757
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908893
  j =  2                              :            45552
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.9946

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.9903


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-5
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.07e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.25e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:38.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.36
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.45
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.97
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17657.32
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.02
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.41
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.10
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.33
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.56
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.19
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.94
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.83
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.47
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.02
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.29
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.74
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.08
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.61
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.53
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.32
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.57
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  442.13
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.02
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4941.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.62
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.45
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.35
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.30
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 9.08e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 8.60e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.22
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    0.31
p-value of test                       : 1 -  2.2e-5    *****

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.31
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.39
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4960.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.27
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11797.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.96
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999981467

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.88
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000017044

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         : -8.34e-3
p-value of test                       :    0.50

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.86
p-value of test                       :    0.19

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.07

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 87  LongestHeadRun, r = 27         1 -  2.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57835525.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5331
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7581
p-value of test                       :  1.2e-3


-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.12
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.73
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.95
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.01
p-value of test                       :  2.9e-3

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.73
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.93
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.51
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.69
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5069.45
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:12.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:56.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45758
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869758
  j =  1                              :        399908489
  j =  2                              :            45748
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908207
  j =  2                              :            45889
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:29.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    3.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.56e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.05e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 2.18e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   43.09
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.25
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.15
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.24
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.78
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.9904

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.80
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  143.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.20
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.23
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.46
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.13
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.36
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.42
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.42
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.56
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.83
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.46
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.04
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.54
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.62
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  153.64
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.14
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.66
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.27
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.23
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.58
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.82
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.82
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.55
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.41
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.24
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.94e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.24e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.51
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.38
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.11
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    4.24
p-value of test                       :  7.0e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4605.30
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4852.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.00
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:24.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3981.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.46
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.94
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:31.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.86
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000099388

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.35
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000004555

Normal statistic for number of bits   :   0.036
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:32.67

 All tests were passed




Server wird beendet - Lösche Semaphor 58851333.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.16
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.89
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     853
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.48
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:13.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    1.10
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.50
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.88
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.80
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.59
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  466.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1338.94
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7343.19
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.94
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:10.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.66
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.75
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5136.39
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:55.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908079
  j =  2                              :            45959
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45975
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869975
  j =  1                              :        399908052
  j =  2                              :            45971
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.62e-3
p-value of test                       :    0.9958

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:29.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  9.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.06
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.44
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.22
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.16
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.76
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.19
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.16
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17754.40
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.20
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.89
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.98
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.32
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.00
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.78
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.56
p-value of test                       :    0.9918


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.73
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.02
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.45
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.70
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.88
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  161.73
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.17
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.41
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.15
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5171.49
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.90
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.71
p-value of test                       :  9.7e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.85
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5020.46
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.51
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.10
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.19
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    1.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.99
p-value of test                       :    0.16

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.81e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.70
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10076.30
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.90
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:04:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.58
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:53.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3990.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11955.95
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.75
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000049861

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.08
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000017815

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.31
p-value of test                       :    0.62

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.18

 All tests were passed




Server wird beendet - Lösche Semaphor 59867141.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5482
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4288
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4335
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9934


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    6.22
p-value of test                       :  7.9e-4    *****

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.67
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.47
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.47
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.73
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7025.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.30
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9904

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.00
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.50
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5009.01
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:00.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908084
  j =  2                              :            45952
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908080
  j =  2                              :            45957
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9919

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.04e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 3.08e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.34
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.97
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17402.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.80
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.02
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.38
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    7.08
p-value of test                       :    0.9997    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.49
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.82
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.22
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.81
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.11
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.49
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.91
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.07
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.03
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.39
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.42
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4954.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.53
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  231.07
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.71
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.53
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.41
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.20
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.72
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.30
p-value of test                       :    0.99

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.98e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 6.41e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.46
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.43
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-3
p-value of test                       :    0.9972

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10281.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.034
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.37
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4256.91
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4201.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.11
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12046.51
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.98
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  8000088348

Normal statistic for number of bits   :    0.70
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.90
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  7999996317

Normal statistic for number of bits   :  -0.029
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.15
p-value of test                       :    0.88

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:15.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.30
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP2, t = 16         7.9e-4
 74  RandomWalk1 R (L=50, r=0)       0.9997 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60915717.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:08.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7490
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.37
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.34
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.70
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.50
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.31
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.19
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.07
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.32
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.60
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.69
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7062.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.83
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:14.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.27
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.84
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4873.53
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:00.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46233
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870233
  j =  1                              :        399907538
  j =  2                              :            46225
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45610
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869610
  j =  1                              :        399908785
  j =  2                              :            45600
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:32.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:20.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.033
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.37
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.37
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.32
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   18.70
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:51.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.12
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.18
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.57
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17470.17
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.68
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.16
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.95
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.83
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.29
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.59
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.28
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.83
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.05
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.21
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.16
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.13
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.15
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.05
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.49
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.28
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.58
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  239.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.82
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.74
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4844.11
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.59
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.90
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.58
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.78
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.39
p-value of test                       :    0.35

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 4.54e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.57
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.54
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.63
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10000.27
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.78
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5006.67
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.63
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11559.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11994.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:34.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.29
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  8000122296

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.46
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000264133

Normal statistic for number of bits   :    2.09
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:30.76

 All tests were passed




Server wird beendet - Lösche Semaphor 61964293.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5402
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7366
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.20
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     548
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.60
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:12.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.63
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.36
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.88
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.82
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.34
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.06
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  226.05
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.81
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7007.68
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.28
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:09.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.64
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4975.59
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:19.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45849
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869849
  j =  1                              :        399908305
  j =  2                              :            45843
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45665
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869665
  j =  1                              :        399908677
  j =  2                              :            45651
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:34.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.72e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:42.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:51.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.51
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.55
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.03
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.53
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.58
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.45
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.42
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.28
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.21
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    8.65
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17449.68
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:55.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.17
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.30
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.76
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.68
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.24
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.14
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.29
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.07
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.75
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  107.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.55
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.99
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.63
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.36
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.45
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.85
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.75
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.46
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.18
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:14.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.50
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.84e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:47.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.26
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.04
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.56e-4
p-value of test                       :    0.9997    *****

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.15
p-value of test                       :  7.3e-3

-----------------------------------------------
CPU time used                    :  00:02:12.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.91
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9999.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10098.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.041
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.55
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3964.79
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.84
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11744.10
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12062.97
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.16
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999933794

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.51
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999872126

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:30.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:35.38

 All tests were passed




Server wird beendet - Lösche Semaphor 42139654.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5400
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7205
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    2.05
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    3.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.69
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.63
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.49
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.88
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.69
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.55
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.79
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  478.37
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.48
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7003.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.27
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   76.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:03:29.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.08
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.54
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:37.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.86
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:20.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:18.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45686
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869686
  j =  1                              :        399908632
  j =  2                              :            45678
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908090
  j =  2                              :            45949
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:32.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.16e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.64e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 2.61e-4
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.92
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.61
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.04
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.18
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.28
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.61
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:41.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17687.53
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.85
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.77
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.89
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.01
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.40
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.17
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.98
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.57
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:40.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.75
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   96.90
p-value of test                       :    0.9994    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.58
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.49
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.35
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.61
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.61
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.62
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.17
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  451.18
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4878.52
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.65
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.09
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.25
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.34
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.77
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.17
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    2.37
p-value of test                       :  8.8e-3



-----------------------------------------------
CPU time used                    :  00:02:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:11.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 7.80e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.24e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.23
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.54
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9977.30
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.36
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.072
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4957.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.18
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.27
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.04
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11972.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.10
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  7999965519

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.43
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999951947

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:57.47
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 M (L=1000, r=0)     0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43319302.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:54.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5438
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4428
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4413
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    3.30
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.78
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.12
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.32
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   87.85
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.47
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1358.98
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7077.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.34
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:17.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.72
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.50
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.31
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46169
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870169
  j =  1                              :        399907671
  j =  2                              :            46151
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908089
  j =  2                              :            45948
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:33.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.42
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9957


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:20.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.80e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.00
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.76
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   48.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.96
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.27
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.25
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:40.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17323.75
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.40
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.95
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.43
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.51
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.38
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   40.60
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.68
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.64
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.26
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.13
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.69
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.68
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.04
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.97
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.51
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.44
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.21
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4866.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.52
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.46
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.86
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.86e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 8.93e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.83e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.81
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.63
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.49
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.37
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10122.48
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.48
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.067
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.075
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.66
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4717.18
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.26
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11754.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11857.11
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.68
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999892382

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.95
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000094042

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.67
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:51.54

 All tests were passed




Server wird beendet - Lösche Semaphor 44597254.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:42.81

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:53.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:44.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1490
p-value of test                       :  4.1e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334610
  j =  1                              :        599997020
  j =  2                              :             1490
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:38.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4360
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7466
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:04:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     621
p-value of test                       :    0.20

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.03
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9932

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.55
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.86
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.45
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.49
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.33
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   27.31
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.27
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.74
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6839.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.58
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.23
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.36
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:38.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5161.43
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:13.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:56.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45971
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869971
  j =  1                              :        399908064
  j =  2                              :            45959
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45846
p-value of test                       :    0.56


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869846
  j =  1                              :        399908312
  j =  2                              :            45838
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:31.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.86e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.063
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.71
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.38
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.39
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.95
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.27
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:02.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.19
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.06
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17666.76
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.74
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.94
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   41.12
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.76
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.19
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.82
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.91
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.89
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.11
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.48
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.93
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  177.73
p-value of test                       :  9.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.36
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.97
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.54
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.41
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.51
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.24
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.79
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.62
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.51
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.55
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  436.28
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.00
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.56
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.40
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 7.47e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.70
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.87
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.22
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.87
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:09.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10133.87
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9847.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4716.84
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4040.69
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11630.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11918.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.45
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000046786

Normal statistic for number of bits   :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.05
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999958271

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.024
p-value of test                       :    0.51

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:43.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           4.1e-4
 33  CouponCollector, r = 27         0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 45678598.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:51.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5350
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4377
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     915
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.64
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.43
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.84
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.41
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.16
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.75
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7234.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.98
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.03
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.30
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:37.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45956
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869956
  j =  1                              :        399908091
  j =  2                              :            45950
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45745
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869745
  j =  1                              :        399908514
  j =  2                              :            45737
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:31.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:19.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.58e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 2.45e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.81
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.21
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:01.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.57
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17395.73
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.59
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.33
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.58
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.03
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.39
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.71
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.84
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.54
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.28
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.11
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.71
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.99
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.18
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.98
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.27
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.95
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.36
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.81
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.22
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.59
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.30
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.61
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.03
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.47
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.65
p-value of test                       :    0.56


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.10e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.39e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.34
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.38
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  182.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9748.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:04:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    3.36
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5101.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.87
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.71
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.45
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11981.75
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.72
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000068317

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:07.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.98
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999988721

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.13
p-value of test                       :    0.55

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.098
p-value of test                       :    0.54

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:43.47

 All tests were passed




Server wird beendet - Lösche Semaphor 46628870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:40.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:05.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7186
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.72

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.01
p-value of test                       :  9.4e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.84
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.98
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.87
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.59
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  224.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7174.04
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.68
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.77
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.23
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5112.53
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:02.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46110
p-value of test                       :    0.14


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870110
  j =  1                              :        399907785
  j =  2                              :            46100
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45834
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869834
  j =  1                              :        399908336
  j =  2                              :            45826
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:19.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.38e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 8.82e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:39.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.21
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.83
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.85
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.17
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.78
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.69
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.82
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.83
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:40.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17114.22
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.59
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.15
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.83
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.82
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.48
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.96
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.67
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.62
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.79
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.99
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.14
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.90
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:43.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.68
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.73
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.09
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  330.19
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.84
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.61
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5090.46
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  421.42
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.87
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.93
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.07e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.55
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.29
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.65
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9851.67
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9934.43
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.07
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:04:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.08
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.62
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4211.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12047.69
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.68
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999990005

Normal statistic for number of bits   :  -0.079
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.86
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999996575

Normal statistic for number of bits   :  -0.027
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.94
p-value of test                       :    0.97

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:14.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.30
p-value of test                       :    0.90

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    2.47
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:01:15.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:51.51

 All tests were passed




Server wird beendet - Lösche Semaphor 47611910.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:39.99

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1481
p-value of test                       :  9.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334601
  j =  1                              :        599997038
  j =  2                              :             1481
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4370
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7078
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:03:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.18
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.20
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.55
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.23
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7156.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.19
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.40
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.51
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.37
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:12.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:54.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45910
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869910
  j =  1                              :        399908182
  j =  2                              :            45906
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45696
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869696
  j =  1                              :        399908608
  j =  2                              :            45696
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 7.99e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.60e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.94e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:37.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.20
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.78
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   41.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.70
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   22.37
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  158.90
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17441.92
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.08
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.82
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.63
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.30
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.55
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.43
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.05
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.49
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.47
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.58
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.37
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.79
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.51
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.56
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.24
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.97
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.37
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.61
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.71
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.81
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.02
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.92
p-value of test                       :    0.71


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.31

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.94e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.66
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:27.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.98
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.72
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9917.38
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9824.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:04:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.76
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4039.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4203.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:32.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12234.55
p-value of test                       :  4.2e-3

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.77
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000029524

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.82
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000112846

Normal statistic for number of bits   :    0.89
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:01.90
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 11  CollisionOver, t = 21           9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48627718.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4453
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7441
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:11.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.10
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:42.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.53
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.39
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.59
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.10
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.76
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6883.28
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.14
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.22
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.99
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:41.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.73
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:56.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45762
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869762
  j =  1                              :        399908477
  j =  2                              :            45760
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907736
  j =  2                              :            46126
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 9.26e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:09.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.88e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 9.93e-5
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.48
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.15
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.73
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.61
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.84
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.42
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.24
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.21
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.37
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.73
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   49.24
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.33
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.13
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.76
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.93
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.21
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.98
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.99
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.70
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.71
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.55
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.07
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.63
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.52
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.44
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.23
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.39
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.22
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  335.58
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.11
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.78
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.43
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    0.71
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.61
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.66e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.09e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.74
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.07
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.84
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10185.22
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10032.14
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.029
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:11.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:33.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4921.11
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4720.09
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11650.56
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11901.15
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.85
p-value of test                       :    0.41


-----------------------------------------------
Total number of bits:  7999873665

Normal statistic for number of bits   :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.32
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  8000038959

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.87
p-value of test                       :    0.97

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:20.88

 All tests were passed




Server wird beendet - Lösche Semaphor 49545222.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:50.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5381
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:41.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    2.31
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     870
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.25
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.91
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1574.16
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:02:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.16
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.91
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   88.45
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4955.46
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:55.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46102
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870102
  j =  1                              :        399907804
  j =  2                              :            46086
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907859
  j =  2                              :            46063
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:29.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.51e-5
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:40.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.49
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.68
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.07
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.13
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.31
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.22
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.75
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17450.19
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.90
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.20
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.62
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.69
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.90
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.70
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  441.27
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.27
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.13
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  193.99
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.30
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.55
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.14
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.58
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.60
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.80
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.33
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.66
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.15
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.24
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4956.24
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.23
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.52
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.54
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.37
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    2.29
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.02e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.90e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.43
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.69
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.06
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  245.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.30
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4017.94
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3827.07
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11924.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12006.46
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.17
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999890951

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.91
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  7999975260

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:35.18
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 98  HammingIndep, L=300, r=26       0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50659353.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9921


-----------------------------------------------
CPU time used                    :  00:00:40.75

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:50.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5439
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7213
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     931
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.60
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:47.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.12
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     637
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.96
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.61
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.54
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:47.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1382.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7101.96
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.61
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   16.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.73
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   16.71
p-value of test                       :  5.1e-3


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.82
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5007.77
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:13.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:57.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45970
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869970
  j =  1                              :        399908069
  j =  2                              :            45952
  j =  3                              :                9
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908520
  j =  2                              :            45734
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:30.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.85e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.26
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.61
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.53
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.54
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.05
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.80
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.07
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.18
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17732.10
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.32
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.66
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.80
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.56
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.85
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.06
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.80
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.67
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  199.55
p-value of test                       :  3.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.35
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.61
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.33
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4999.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.28
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.76
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.94
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.48
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.39
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.34
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.94
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.49e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.78e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.82
p-value of test                       :    0.99

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.00
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.75
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.54
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9774.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9820.09
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.047
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4973.98
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9913

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4002.79
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.08
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.57
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:31.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12018.99
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.07
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000071371

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.95
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999991103

Normal statistic for number of bits   :  -0.070
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         : 8.72e-3
p-value of test                       :    0.50

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:16.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:38.85
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    3.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 51675161.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:51.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.65
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     917
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.21
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.05
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.56
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     182
p-value of test                       :  6.2e-3

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.72
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.22
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.67
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.16
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.22
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.87
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:24.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.70
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.45
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.43
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:13.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:57.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46252
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870252
  j =  1                              :        399907500
  j =  2                              :            46244
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45786
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869786
  j =  1                              :        399908431
  j =  2                              :            45780
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 9.75e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:29.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:46.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.05e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 1.42e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.058
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.069
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.51
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   68.12
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:00:49.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.69
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.78
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.34
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17525.08
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.07
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.66
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.42
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.79
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.61
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.63
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.51
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.64
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.72
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.34
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.85
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.29
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.25
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.36
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5065.30
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.36
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.70
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.82
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.27
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4922.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.11
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.90
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.70
p-value of test                       :    0.47


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.94
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.95
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:22.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.74
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.76
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10146.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4986.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.16
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4140.01
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:34.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.04
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000080794

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.15
p-value of test                       :    0.83


-----------------------------------------------
Total number of bits:  8000054952

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.08

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:53.77

 All tests were passed




Server wird beendet - Lösche Semaphor 52690969.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4494
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:01:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4424
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7230
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7176
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     264
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:12.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.40
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.35
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.63
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1307.96
p-value of test                       :    0.9933

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6862.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.30
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:08.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.42
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.72
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:35.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5044.96
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:55.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46060
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870060
  j =  1                              :        399907884
  j =  2                              :            46052
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46068
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870068
  j =  1                              :        399907866
  j =  2                              :            46064
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:39.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.06
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.54
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.29
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.75
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.48
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17237.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.34
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   44.10
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.18
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.36
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.18
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.92
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.37
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.36
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.21
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.86
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.11
p-value of test                       :  7.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.36
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  160.95
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.47
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.96
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.03
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5152.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.71
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.95
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5119.83
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.74
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.76
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.64
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.83
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 8.47e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:47.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.35
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.31
p-value of test                       :    0.83

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.50
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.47
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:10.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.75
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3999.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4011.10
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.01
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:34.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11844.30
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.67
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  8000006805

Normal statistic for number of bits   :   0.054
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.93
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999807182

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    2.39
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:16.04

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.39

 All tests were passed




Server wird beendet - Lösche Semaphor 53641241.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4501
p-value of test                       :  6.7e-3


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:11.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:09.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.86
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:48.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:14.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.18
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.26
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     338
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.92
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.95
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.57
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:13.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.16
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7035.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.91
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:09.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:47.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.40
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5075.15
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:00.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46051
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870051
  j =  1                              :        399907900
  j =  2                              :            46047
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.17

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45840
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869840
  j =  1                              :        399908322
  j =  2                              :            45836
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:30.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9942

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.22e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   56.02
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.87
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.01
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.84
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.01
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.38
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17558.07
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.41
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.99
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.52
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.76
p-value of test                       :    0.9921


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.14
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.13
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.35
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.91
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.03
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.57
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.70
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.14
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.53
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.96
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.67
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.20
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.74
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.91
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.28
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.97
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.63
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.26
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.31
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.58
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.06
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.04
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.82e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.42
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:34.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:18.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10290.82
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.30
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.85
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      : -6.84e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:40.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5049.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:52.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.20
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.02
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.62
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000024826

Normal statistic for number of bits   :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.06
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000009322

Normal statistic for number of bits   :   0.074
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:20.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.18

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:27.81

 All tests were passed




Server wird beendet - Lösche Semaphor 54657049.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5298
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4343
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7463
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.95
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.14
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:20.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    2.61
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.00
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.40
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.14
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.92
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.46
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.36
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.44
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.33
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.68
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.44
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.92
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6956.69
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.56
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:10.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.96
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4904.45
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:03.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45928
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869928
  j =  1                              :        399908147
  j =  2                              :            45922
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908434
  j =  2                              :            45777
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:51.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-4
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:26.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:01.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.18
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.49
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.67
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.10
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.29
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.00
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.94
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.50
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17417.71
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.88
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.77
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.27
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.55
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.47
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.57
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.52
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.09
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.28
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.82
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.84
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.72
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.21
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.81
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.43
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  521.04
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.18
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.82
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4880.34
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.95
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.44
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.46
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5134.57
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.90
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.48
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.20
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.88e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.22e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 6.76e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.39
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.99
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9997    *****

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.22
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:29.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  164.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:29.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10110.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9986.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:00.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.62
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5009.00
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4165.28
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4096.47
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.84
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:34.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.58
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.61
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  8000114895

Normal statistic for number of bits   :    0.91
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:16.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.20
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000046150

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.74
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:53.80

 All tests were passed




Server wird beendet - Lösche Semaphor 56000537.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:52.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:11.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7428
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7510
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.65
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.88
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.17
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.53
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.56
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.45
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.58
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.91
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.61
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  481.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1419.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.8e-3

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.37
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.82
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  136.81
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.58
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46014
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870014
  j =  1                              :        399907978
  j =  2                              :            46002
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45545
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869545
  j =  1                              :        399908914
  j =  2                              :            45537
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9909

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    3.48
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.46e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.076
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:44.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.81
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.22
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.20
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.58
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.52
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.36
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.32
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  108.63
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17621.65
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.62
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.29
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.01
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.34
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.48
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.70
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.04
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.17
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.82
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.69
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  522.87
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.69
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.71
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  318.56
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5278.21
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.39
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.16
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  328.43
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.15
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5102.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.23
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.72
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.23
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.54
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.33
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.34

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.59e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 4.82e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.34
p-value of test                       :    0.31

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.83
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.81
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.56
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9996    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4878.51
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4977.19
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4057.16
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11622.84
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12050.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.33
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000104704

Normal statistic for number of bits   :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.46
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999946076

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.4e-3

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.30
p-value of test                       :    0.01

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.38

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:15.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:26.77

 All tests were passed




Server wird beendet - Lösche Semaphor 57409561.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:41.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:52.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4511
p-value of test                       :  4.4e-3


-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4319
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:04:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.22
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.50
p-value of test                       :  9.9e-3

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.65
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.72
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.51
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  458.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.51
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7071.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  139.36
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5092.34
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:03.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908167
  j =  2                              :            45912
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45713
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869713
  j =  1                              :        399908575
  j =  2                              :            45711
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:30.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 2.39e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.93e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.02
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.45
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.17
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.17
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.99
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17600.88
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.41
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.82
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.06
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.59
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.45
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.03
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.48
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.24
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.31
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.65
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.25
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.44
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.56
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.27
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.07
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5098.16
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.60
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.92
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.31
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.88
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.10
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.23
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :  -0.042
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.51
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.016
p-value of test                       :    0.49

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.80e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.96e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.70
p-value of test                       :    0.46

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.65
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.40
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9989.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.52
p-value of test                       :  2.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9740.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:18.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5011.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3986.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4229.28
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.73
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.67
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.54
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000028978

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999777179

Normal statistic for number of bits   :   -1.76
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.94
p-value of test                       :    0.17

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:30.81

 All tests were passed




Server wird beendet - Lösche Semaphor 58458137.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:41.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5461
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:10.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     859
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    2.92
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     605
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    2.98
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.71
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.53
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.06
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.62
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  413.34
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1415.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6904.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.84
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.99
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:16.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.59
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.52
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.55
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:03.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45699
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869699
  j =  1                              :        399908605
  j =  2                              :            45693
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45766
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869766
  j =  1                              :        399908472
  j =  2                              :            45758
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.13e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.05
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.50
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.28
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.80
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.68
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.04
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.07
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.43
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.78
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.39
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.96
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.24
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.74
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.77
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.03
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.94
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.84
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.75
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.03
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.30
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.62
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.13
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4971.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.64
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.46
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.97
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.08
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.65
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.21
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -1.16
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.18
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   0.097
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.50e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.77
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.41
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.46
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.34
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10217.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.80
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.69
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4793.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4130.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:28.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11926.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12170.80
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.68
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999928949

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.73
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000054679

Normal statistic for number of bits   :    0.43
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:06.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.64
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:28.13

 All tests were passed




Server wird beendet - Lösche Semaphor 59473945.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5236
p-value of test                       :    0.9941


-----------------------------------------------
CPU time used                    :  00:03:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7151
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7571
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:04:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.55
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.51
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.81
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:15.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.34
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.27
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.65
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.29
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:09.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.50
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.58
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.25
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  363.87
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1351.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6983.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 3.55e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    3.45
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.52e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.61
p-value of test                       :  1.9e-4    *****

Anderson-Darling statistic = A2       :    4.92
p-value of test                       :  3.3e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   95.23
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5165.34
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908223
  j =  2                              :            45884
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.75

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45957
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869957
  j =  1                              :        399908088
  j =  2                              :            45953
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 4.75e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:37.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.19
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.13
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.98
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.34
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.25
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.30
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.50
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.91
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:40.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17285.35
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.58
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.93
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.78
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.63
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.98
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.62
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.51
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.82
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.67
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.14
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.13
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.44
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.98
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.85
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.52
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.56
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5054.77
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.31
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.34
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.59
p-value of test                       :  6.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4964.99
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  411.68
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.64
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   0.030
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.45
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.85e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.94e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.24
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.46
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.38
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.9e-3

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.68
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9970.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.52
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4255.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.96
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11693.52
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:34.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.30
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  8000005275

Normal statistic for number of bits   :   0.042
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.55
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  8000055426

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.55
p-value of test                       :    0.06

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:22.31

 All tests were passed




Server wird beendet - Lösche Semaphor 60588057.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:52.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4272
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4240
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     907
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    3.18
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     259
p-value of test                       :    0.9914

Stat. AD (mNP2)                       :    3.15
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:17.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.43
p-value of test                       :    0.82

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.09
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.10
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.48
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:11.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.32
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.89
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  214.66
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1500.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7018.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.41
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:08.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.46
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.22
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5172.41
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:14.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45827
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869827
  j =  1                              :        399908349
  j =  2                              :            45821
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45569
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869569
  j =  1                              :        399908868
  j =  2                              :            45557
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 6.30e-3
p-value of test                       :    0.9919

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:30.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -2.51
p-value of test                       :    0.9939

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.78
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:41.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.65
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.18
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.84
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.53
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:47.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.07
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.52
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.58
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17295.60
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.94
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.39
p-value of test                       :    0.9966


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.56
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.61
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.08
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.79
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.74
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.42
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.06
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.47
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.25
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.22
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.47
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.63
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.50
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5146.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.03
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.96
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.98
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.08
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5143.59
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.23
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:02:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.69e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.90
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.22
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.01
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.66
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4103.25
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4182.24
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11821.84
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11809.20
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.22
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999832523

Normal statistic for number of bits   :   -1.32
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.15
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999944597

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.72e-3
p-value of test                       :    0.9917

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:11.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.68

 All tests were passed




Server wird beendet - Lösche Semaphor 61603865.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:41.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:52.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5301
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:41.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:02.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:04:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    3.55
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.30
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.91
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.96
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.70
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6849.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.30
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.62
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  160.64
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.19
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:09.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45893
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869893
  j =  1                              :        399908216
  j =  2                              :            45889
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45710
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869710
  j =  1                              :        399908581
  j =  2                              :            45708
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:03.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -1.36e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.82
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.85
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   47.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.29
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.54
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:28.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.72
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:01:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17594.92
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.70
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.58
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.19
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.07
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.07
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.47
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.29
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.34
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.18
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.97
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  407.74
p-value of test                       :    0.9990    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.83
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.71
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.91
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.45
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.26
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.02
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.31
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.63
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.10
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.59
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.87
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.86
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.72
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.15
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:02:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.027
p-value of test                       :    0.49

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:14.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.62e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 8.06e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 8.37e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.13
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.29
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.43
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.11
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10130.16
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:03:30.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4932.20
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4990.12
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.10
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3960.54
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.61
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11899.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.16
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999974072

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:00:58.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   38.48
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999926345

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.18
p-value of test                       :    0.88

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:16.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         : 6.84e-3
p-value of test                       :    0.50

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:04:32.45
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62652441.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5413
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7287
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7212
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     889
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:52.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:16.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.16
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.83
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     333
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:11.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.76
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.10
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.63
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.25
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:11.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.79
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.31
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.53
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  266.99
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7099.66
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.69
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.06
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:03:09.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.04
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.53
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:38.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:16.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45659
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869659
  j =  1                              :        399908686
  j =  2                              :            45651
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45775
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869775
  j =  1                              :        399908452
  j =  2                              :            45771
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:31.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-3
p-value of test                       :    0.9986

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:34.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.71e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.44e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.93
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.00
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:57.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.43
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  164.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9984

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.49
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.75
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.74
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.48
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.73
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.87
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.20
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.95
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.89
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.25
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.56
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.77
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.30
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.98
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:49.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.05
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.65
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.75
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.24
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.65
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4741.33
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.07
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  168.17
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.17
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.34
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.95
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.68
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.83
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.21
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:14.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:10.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    2.45
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 8.62e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.14e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.63
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.55
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.14
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:11.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  206.64
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:11.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.76
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10195.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.80
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.28
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4820.12
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.34
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4127.89
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11626.60
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11730.82
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.85
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999890381

Normal statistic for number of bits   :   -0.87
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.83
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000131821

Normal statistic for number of bits   :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.46
p-value of test                       :    0.07

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.84
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.21
p-value of test                       :    0.01

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.79
p-value of test                       :    0.79

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.91
p-value of test                       :    0.18

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:53.01

 All tests were passed




Server wird beendet - Lösche Semaphor 42172423.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:12.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1464
p-value of test                       :  3.9e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334584
  j =  1                              :        599997072
  j =  2                              :             1464
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:27.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:34.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5249
p-value of test                       :    0.9903


-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:35.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4432
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7444
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.32
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     881
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.61
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     585
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    3.15
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.94
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.55
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   31.44
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.86
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.94
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  232.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  370.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.89
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7343.52
p-value of test                       :  6.6e-3

-----------------------------------------------
CPU time used                    :  00:01:50.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.61
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:37.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5033.59
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:17.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:16.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46168
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870168
  j =  1                              :        399907665
  j =  2                              :            46166
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45757
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869757
  j =  1                              :        399908488
  j =  2                              :            45753
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:31.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.08
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.05e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.060
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.23
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.70
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.73
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.31
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:31.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.90
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.23
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.58
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.08
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:40.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   15.84
p-value of test                       :    0.9986


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.63
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.47
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.07
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.49
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.69
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.02
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.89
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.96
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.10
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.23
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.93
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.82
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.18
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.84
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.46
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.38
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4931.62
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.78
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.28
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.55
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.28
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:15.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.66
p-value of test                       :    0.26

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.13
p-value of test                       :    0.13

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 5.97e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.12e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.19
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.48
p-value of test                       :    0.23

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.60e-4
p-value of test                       :    0.9995    *****

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.71
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  262.40
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:02:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.69
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10170.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:59.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.087
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:04:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.06e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  3.6e-3

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5106.55
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4224.29
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.99
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.59
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000081133

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.66
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000005221

Normal statistic for number of bits   :   0.041
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   0.021
p-value of test                       :    0.49

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.46
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.94

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:37.67

 All tests were passed




Server wird beendet - Lösche Semaphor 43253776.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:54.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1452
p-value of test                       :  9.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334572
  j =  1                              :        599997096
  j =  2                              :             1452
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:38.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7451
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7388
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:04:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:11.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.44
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.02
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.45
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.27
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.87
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.48
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  452.03
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.32
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:09.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.63
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.77
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.93
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.75
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.33
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:17.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908560
  j =  2                              :            45714
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908036
  j =  2                              :            45976
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:33.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.79e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 7.88e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.44
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.27
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.53
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.12
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.05
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.60
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:40.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.40
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.47
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.94
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.93
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.23
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.55
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.86
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   60.42
p-value of test                       :  4.8e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.15
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.49
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.57
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.50
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  111.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.52
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.27
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.17
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.59
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.91
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.73
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.24
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4943.12
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.86
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.54
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.58
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4902.89
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.78
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.89
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.78
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    2.08
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.46
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   0.082
p-value of test                       :    0.47

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.39e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.74
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.10
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.54
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.81
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9926.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:29.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4681.55
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.60
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4300.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12043.54
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11954.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.89
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000109990

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.55
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999915236

Normal statistic for number of bits   :   -0.67
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.59e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.66
p-value of test                       :    0.9961

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:53.55

 All tests were passed




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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:41.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:45.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:08.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5368
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     874
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     631
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.51
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.00
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.53
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.39
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.83
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.75
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.39
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.60
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  216.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:54.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1456.26
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7112.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.15
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:03:15.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.84
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.08
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:40.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5128.62
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46041
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870041
  j =  1                              :        399907924
  j =  2                              :            46029
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45813
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869813
  j =  1                              :        399908378
  j =  2                              :            45805
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:32.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:21.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.40e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.68e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.89e-4
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 8.31e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.33
p-value of test                       :    0.9901

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.81
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.75
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.81
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.13
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:29.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.94
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.43
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.65
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.78
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.21
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.83
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.10
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.63
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.99
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:38.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.25
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   56.48
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.57
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.95
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.81
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.99
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.90
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  463.11
p-value of test                       :  3.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.57
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.37
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  216.84
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.29
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.95
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.22
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.25
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.93
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.77
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.72
p-value of test                       :    0.55


-----------------------------------------------
Normal statistic for number of jumps  :  -0.073
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:25.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.28
p-value of test                       :    0.10

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :  -0.082
p-value of test                       :    0.53

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.31e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 4.26e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.17
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.47
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.90
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10048.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -3.02
p-value of test                       :    0.9988

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.54
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:30.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5043.25
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.21
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.56
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4110.97
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.01
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12029.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000103378

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:09.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.90
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999990122

Normal statistic for number of bits   :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:15.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:55.05

 All tests were passed




Server wird beendet - Lösche Semaphor 45645840.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5452
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7397
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    2.14
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.21
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     575
p-value of test                       :    0.84

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:13.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.40
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   17.38
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.38
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.12
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  240.57
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  468.39
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.26
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:02.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7037.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:16.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.83
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.50
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.52
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5084.40
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:02.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45272
p-value of test                       :    0.9977


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869272
  j =  1                              :        399909458
  j =  2                              :            45268
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46215
p-value of test                       :    0.06


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870215
  j =  1                              :        399907575
  j =  2                              :            46205
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:30.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:20.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.92e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.71
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:50.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.72
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.97
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.22
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9922

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.26
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.06
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.21
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17271.81
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.06
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.72
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.80
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.76
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.91
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.29
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.34
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.03
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.67
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.54
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.79
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.55
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.62
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.46
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.25
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5122.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.76
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.87
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.95
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4768.91
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  431.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.55
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.33
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -0.48
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.92
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    2.39
p-value of test                       :  8.5e-3



-----------------------------------------------
CPU time used                    :  00:02:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.98
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 9.21e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 4.11e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.26
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.38
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.04
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.81
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.14
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5085.18
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12165.91
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11905.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:31.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.83
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  7999984974

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.04
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000024562

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:02.39

 All tests were passed




Server wird beendet - Lösche Semaphor 46858256.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:55.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7226
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.54
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     837
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     649
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:14.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.75
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.19
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.44
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  441.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6976.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.45
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:08.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.90
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.70
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4838.44
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:06.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45519
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869519
  j =  1                              :        399908962
  j =  2                              :            45519
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46250
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870250
  j =  1                              :        399907506
  j =  2                              :            46238
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-5
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.58
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.59
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.60
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.35
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.61
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.95
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.61
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:28.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17447.26
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:00:54.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   57.22
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.38
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.09
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.43
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.50
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.92
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.80
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.87
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.69
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.75
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  216.08
p-value of test                       :  1.5e-5    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.41
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  104.42
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.70
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.76
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.56
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.40
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5117.85
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.95
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.37
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.34
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.82
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.24
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.66
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.42e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 8.17e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.97e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   17.83
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.40
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10039.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10097.31
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : -7.75e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:19.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4864.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4072.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.05
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11950.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12086.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.19
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999983543

Normal statistic for number of bits   :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.93
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  7999963377

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.84

Sample variance                       :    1.52
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:12.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.59
p-value of test                       :    0.28

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:12.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:31.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 R (L=1000, r=0)     1.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47808528.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:41.29

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:52.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:54.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:27.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7445
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.43
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9940


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:13.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.61
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.15
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.17
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.52
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.16
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.87
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.96
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.40
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:35.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5207.00
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:00.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46026
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870026
  j =  1                              :        399907952
  j =  2                              :            46018
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908113
  j =  2                              :            45939
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:32.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:19.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 5.82e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.66e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.22
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.49
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.88
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.12
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.11
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.58
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.62
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   11.30
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:19.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.45
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17428.01
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:53.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.14
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.65
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.51
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.14
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.10
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.42
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.94
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.99
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.85
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.87
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.93
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.96
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.39
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.27
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.14
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.58
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4787.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.86
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.16
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5003.15
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  424.13
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.87
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.93
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :  -0.027
p-value of test                       :    0.51

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.81e-3
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.64e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 7.40e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.80
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.64
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.95
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10088.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10310.73
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.24
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:04:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5083.39
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:53.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.88
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.08
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:32.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11949.54
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.04
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000094225

Normal statistic for number of bits   :    0.74
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.51
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000037990

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.80
p-value of test                       :    0.96

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:11.55

 All tests were passed




Server wird beendet - Lösche Semaphor 48824336.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:40.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:39.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4280
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     958
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     592
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9919


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.82
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:42.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.99
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.26
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.15
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  180.29
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1428.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7110.24
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.58
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:07.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.11
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.19
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5093.49
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.88

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46012
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870012
  j =  1                              :        399907978
  j =  2                              :            46008
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908223
  j =  2                              :            45884
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 9.64e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.73
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.75
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.47
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.6e-3

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:28.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.09
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17350.65
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:00:53.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.97
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.05
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   41.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.64
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.78
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.68
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.12
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.90
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:37.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.57
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.22
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.11
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.64
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.00
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.40
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.14
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5004.40
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.21
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.42
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.44
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.62
p-value of test                       :    0.73


-----------------------------------------------
Normal statistic for number of jumps  :    0.84
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.31
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:25.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.41

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.52e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 5.18e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.22e-3
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.31
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.29
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.39
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.92
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9718.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.062
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4911.50
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4895.43
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.92
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4020.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.94
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:31.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.75
p-value of test                       :  3.9e-3


-----------------------------------------------
Total number of bits:  7999955460

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.36
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999954326

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.21

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.49
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    0.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.32

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:26.18

 All tests were passed




Server wird beendet - Lösche Semaphor 49774608.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:10.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1280
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334400
  j =  1                              :        599997440
  j =  2                              :             1280
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5468
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:54.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4297
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4345
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    2.39
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.56
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:12.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:40.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.99
p-value of test                       :  8.2e-3

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.44
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.16
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.04
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1489.96
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7087.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.56
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:08.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.76
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.61
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4939.24
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908039
  j =  2                              :            45973
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45902
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869902
  j =  1                              :        399908198
  j =  2                              :            45898
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.71
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:17.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-5
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 1.86e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:42.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.96
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.85
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.13
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.69
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.12
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.98
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.65
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.42
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.29
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17335.27
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.62
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.04
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.68
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.09
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   18.04
p-value of test                       :    0.9946


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.05
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.13
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.02
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.75
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.01
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.51
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.74
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.00
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.96
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  580.11
p-value of test                       :  7.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.60
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.65
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  448.03
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.96
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.99
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.85
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.19
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4987.59
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.15
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.54
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.83
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.59
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         : -5.43e-3
p-value of test                       :    0.50

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.65
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.80
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.31
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.34
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.44
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:04:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5048.45
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4765.64
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.40
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:31.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.32
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999959669

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.10
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999939644

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.055
p-value of test                       :    0.52

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :  -0.077
p-value of test                       :    0.53

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.84

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:12.20

 All tests were passed




Server wird beendet - Lösche Semaphor 50823184.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:40.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:05.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.78
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.29
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.75
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    2.27
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9946


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.04
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:11.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.22
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:12.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.08
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.37
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  250.53
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1340.61
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7078.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.21
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.24
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:18.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.28
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.10
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5123.17
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:24.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908212
  j =  2                              :            45888
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45958
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869958
  j =  1                              :        399908086
  j =  2                              :            45954
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:33.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.23e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.98
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.56
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:52.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.36
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.04
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.34
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.35
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.20
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.83
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   90.01
p-value of test                       :    0.9970

-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17079.59
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.32
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.92
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.35
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.45
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.89
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.31
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.81
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.92
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.18
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.19
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.12
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.93
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.91
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.53
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.80
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.89
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.40
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  419.49
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.94
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.63
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.41
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.30
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.93
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.96
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -1.89
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.46
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :    1.48
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 9.10e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.47e-3
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.13
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.77
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.46
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10132.26
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4961.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:00.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.71
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.30
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.13
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.74
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.26
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999934670

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.68
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999941954

Normal statistic for number of bits   :   -0.46
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    1.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.69
p-value of test                       :    0.95

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:06.34

 All tests were passed




Server wird beendet - Lösche Semaphor 51871760.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.40

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5410
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9963


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:11.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:41.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.59
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  192.96
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  450.69
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1371.72
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7000.75
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.78
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.55
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.54
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5148.42
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:59.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908034
  j =  2                              :            45980
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908120
  j =  2                              :            45934
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:29.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.84e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.17
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.36
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.84
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.96
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.14
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.67
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.05
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.31
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17708.73
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.44
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.02
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.85
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.98
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.78
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   59.48
p-value of test                       :  6.1e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.03
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.18
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.28
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.18
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.93
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.37
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  102.14
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.71
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.64
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.05
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5086.74
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.85
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.68
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.15
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.46
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.07
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :   -1.35
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.35
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.49
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :   -0.78
p-value of test                       :    0.78

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.50
p-value of test                       :    0.93

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 2.51e-3
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 6.36e-3
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.87
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.44
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.75
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.43e-3
p-value of test                       :    0.9909

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10214.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.60
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:20.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5001.28
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5010.41
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4273.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.86
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12005.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11793.10
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.69
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999977741

Normal statistic for number of bits   :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.20
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000016630

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    2.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:38.93

 All tests were passed




Server wird beendet - Lösche Semaphor 52854800.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:40.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:00:52.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5506
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4361
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4409
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4384
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7478
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     319
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     125
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.49
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.76
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.10
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  272.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.53
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1367.20
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7081.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.23
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:08.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.29
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.66
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5283.41
p-value of test                       :  8.1e-3


-----------------------------------------------
CPU time used                    :  00:01:13.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:59.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45779
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869779
  j =  1                              :        399908446
  j =  2                              :            45771
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45568
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869568
  j =  1                              :        399908867
  j =  2                              :            45562
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 3.65e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.11
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.52
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.51
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.89
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.08
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.49
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.28
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.06
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17534.21
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.31
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.25
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.24
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.60
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.82
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.57
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.58
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.01
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.64
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.60
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   94.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.16
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  107.86
p-value of test                       :    0.9923


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.38
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.14
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.39
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.76
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.46
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.80
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.36
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5230.47
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  344.79
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.61
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.84
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:02:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.04
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.21
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.96
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.13e-3
p-value of test                       :    0.9946

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10107.06
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9734.10
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.045
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5072.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4257.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.07
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11748.32
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.60
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000070534

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   97.81
p-value of test                       :  2.5e-4    *****


-----------------------------------------------
Total number of bits:  7999813851

Normal statistic for number of bits   :   -1.47
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.65
p-value of test                       :    0.74

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:14.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:34.69
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             2.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53968912.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:40.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1455
p-value of test                       :  7.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334575
  j =  1                              :        599997090
  j =  2                              :             1455
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:54.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4474
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4419
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7513
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:11.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.18
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.53
p-value of test                       :    0.71

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    2.70
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:41.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.02
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.00
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.85
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:26.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.28
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  298.01
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:01:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  440.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1598.89
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:02:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6987.23
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   36.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.14
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:18.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.84
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.39
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46106
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870106
  j =  1                              :        399907793
  j =  2                              :            46096
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45862
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869862
  j =  1                              :        399908277
  j =  2                              :            45860
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 4.80e-3
p-value of test                       :    0.9942

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:33.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.46
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:48.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.65
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.84
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.39
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.01
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.38
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.88
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.95
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17291.38
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:00:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.85
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.97
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.97
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.30
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.11
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.39
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.20
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.04
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.31
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.00
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  436.93
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.06
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.14
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.55
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.84
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.64
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4957.57
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.71
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.53
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.20
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.78
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5071.26
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.54
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.85
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.85
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.76
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.46
p-value of test                       :    0.68

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.79
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.67
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.41
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.17
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.70
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10181.02
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.89
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  6.8e-3

Anderson-Darling statistic = A2       :    2.61
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5090.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.92
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11850.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.20
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.92
p-value of test                       :    0.11


-----------------------------------------------
Total number of bits:  7999856814

Normal statistic for number of bits   :   -1.13
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.92
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000036868

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.17
p-value of test                       :    0.88

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:52.82

 All tests were passed




Server wird beendet - Lösche Semaphor 54984720.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:40.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:50.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1442
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334562
  j =  1                              :        599997116
  j =  2                              :             1442
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5454
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4493
p-value of test                       :  9.3e-3


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    3.63
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:47.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.17
p-value of test                       :    0.9968

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     160
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.93
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.70
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.62
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.76
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  204.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.11
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1523.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7059.22
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.30
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:16.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.83
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:03:18.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.39
p-value of test                       :    0.9955


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.14
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5028.97
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46017
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870017
  j =  1                              :        399907971
  j =  2                              :            46007
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45406
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869406
  j =  1                              :        399909195
  j =  2                              :            45392
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:20.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:52.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.84e-4
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.35e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.46
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:47.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.41
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.74
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.36
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.79
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17575.45
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.72
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.61
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.88
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.70
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.34
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.27
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.71
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.94
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.20
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.29
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.22
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.80
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.71
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.38
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.91
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.75
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.32
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4859.35
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.27
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.61
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.26
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.17
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  448.28
p-value of test                       :  7.4e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  237.57
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.27
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.45
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.62

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.80e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.19e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.60
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.97
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.08
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.99
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9981.59
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:04:29.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4945.28
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4335.50
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:28.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11866.83
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12105.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.52
p-value of test                       :  5.0e-3


-----------------------------------------------
Total number of bits:  7999781427

Normal statistic for number of bits   :   -1.73
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.47
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999921410

Normal statistic for number of bits   :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.32
p-value of test                       :    0.91

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:19.29

 All tests were passed




Server wird beendet - Lösche Semaphor 56066064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1471
p-value of test                       :  2.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334591
  j =  1                              :        599997058
  j =  2                              :             1471
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:41.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7162
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.78
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     608
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.48
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.63
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.46
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.93
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.40
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1445.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6927.35
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.04
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:21.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:03:24.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.57
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.06
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4917.92
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:58.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908068
  j =  2                              :            45963
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45790
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869790
  j =  1                              :        399908424
  j =  2                              :            45782
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:30.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    4.26
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.20e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.10
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.85
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.05
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.05
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.69
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.70
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:28.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.49
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.47
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.61
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.42
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.94
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.75
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.17
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.41
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.55
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.73
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:45.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.70
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.12
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.68
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.85
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.82
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.63
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.33
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5072.29
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.40
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.52
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.35
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.73
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5262.33
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.96
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.95
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.17
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -3.01
p-value of test                       :    0.9987



-----------------------------------------------
CPU time used                    :  00:02:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.35
p-value of test                       :    0.36

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.61e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 4.87e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:46.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.19
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.15
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.04
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10013.57
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10199.55
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:04:18.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.5e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5073.59
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.64
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4134.95
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12028.88
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.72
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.84
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000002320

Normal statistic for number of bits   :   0.018
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.10
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999905117

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:43.86

 All tests were passed




Server wird beendet - Lösche Semaphor 57212944.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4312
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:00.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.31
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    2.37
p-value of test                       :    0.06

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     576
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    3.08
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.41
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     304
p-value of test                       :    0.42

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.28
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.79
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.03
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.90
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1401.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6840.07
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.16
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.58
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.27
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.44
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:36.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:01.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45593
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869593
  j =  1                              :        399908820
  j =  2                              :            45581
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908131
  j =  2                              :            45924
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.9934

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.06e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 2.68e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:00:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.24
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.89
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.08
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.29
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:28.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.62
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17203.30
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.68
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   58.10
p-value of test                       :  8.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.81
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.50
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.63
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.63
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.42
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.70
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.53
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  113.55
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.48
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.85
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.05
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.68
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.19
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.23
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.83
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.85
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4883.89
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.67
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.44
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.33
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.14
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.16
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.46
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.59
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.74
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.04
p-value of test                       :    0.30


-----------------------------------------------
Normal statistic for number of jumps  :   -1.41
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.81
p-value of test                       :    0.97

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 6.29e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 7.75e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.92
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.53
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.52
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9890.08
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9826.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:02.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:04:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4928.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.42
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4243.46
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11726.73
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:32.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11900.16
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.99
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  8000038437

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.16
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999955967

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:54.39

 All tests were passed




Server wird beendet - Lösche Semaphor 58228752.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5434
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7233
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.76
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.19
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.07
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:13.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.18
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.28
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.60
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.91
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.79
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.69
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.94
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.40
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.42
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5030.54
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:01.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46082
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870082
  j =  1                              :        399907843
  j =  2                              :            46068
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45896
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869896
  j =  1                              :        399908211
  j =  2                              :            45890
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:31.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :  5.7e-3

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:19.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 9.66e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.60e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.27
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.93
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.69
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.69
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.61
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17181.98
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.70
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.56
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.32
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.09
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.55
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   44.67
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.59
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.55
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.87
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.97
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.50
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  181.83
p-value of test                       :  5.3e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.85
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.14
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.29
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  542.19
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.60
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.40
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.47
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.20
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.07
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  420.53
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  253.60
p-value of test                       :  6.1e-3


-----------------------------------------------
CPU time used                    :  00:00:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.22
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.11
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.17
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.64
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.93
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9839.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10121.97
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.2e-3

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5064.04
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:52.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.40
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.76
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4194.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11911.61
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11935.75
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.23
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  7999987917

Normal statistic for number of bits   :  -0.096
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.10
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  7999846152

Normal statistic for number of bits   :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:01:07.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:10.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.27
p-value of test                       :    0.10

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:45.37

 All tests were passed




Server wird beendet - Lösche Semaphor 59179024.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4287
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     567
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    3.57
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     341
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.66
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.49
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.05
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.51
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:29.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  428.62
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7121.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.11
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   80.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:18.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.52
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.43
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.63
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:57.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45305
p-value of test                       :    0.9964


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869305
  j =  1                              :        399909393
  j =  2                              :            45299
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908710
  j =  2                              :            45642
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:16.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:38.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.91e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.51e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.65
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.03
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:51.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.38
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.47
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.32
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.29
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.96
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.65
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  147.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17161.15
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.92
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.30
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.11
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.69
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.93
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.96
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.50
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.84
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.37
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.70
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.91
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.64
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.35
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  493.07
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.68
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.13
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.85
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.87
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  164.09
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.79
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.40
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.30
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.31
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.61
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.46
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.95e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.91
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  167.90
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9893.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.89
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:05:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.12
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4154.88
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4281.43
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12118.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11975.82
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.23
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  8000116110

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.12
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  7999950306

Normal statistic for number of bits   :   -0.39
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:19.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.81
p-value of test                       :    0.79

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:51.60

 All tests were passed




Server wird beendet - Lösche Semaphor 60162064.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:06.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1465
p-value of test                       :  3.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334585
  j =  1                              :        599997070
  j =  2                              :             1465
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1298
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334418
  j =  1                              :        599997404
  j =  2                              :             1298
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5521
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7159
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7256
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:04:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.03
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.41
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:41.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.00
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.02
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   26.01
p-value of test                       :    0.9995    *****

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.53
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   89.39
p-value of test                       :  1.7e-3

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  436.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1477.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7116.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   79.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.20
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:40.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5159.72
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:30.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45791
p-value of test                       :    0.66


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869791
  j =  1                              :        399908422
  j =  2                              :            45783
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45613
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869613
  j =  1                              :        399908777
  j =  2                              :            45607
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:19.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.67e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 1.61e-4
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:43.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:56.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.22
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.35
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.72
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.94
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17498.52
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.72
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.07
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.91
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.50
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.07
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.12
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.76
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   48.52
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.03
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.99
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.28
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  463.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.85
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.75
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.57
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.77
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.09
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.11
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.59
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.62
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.34
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.95
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.14
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4969.55
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.20
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.50
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.90
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.25
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :    1.02
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.27e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.51e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.43e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.86
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:33.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.87
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.16
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:28.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.36
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.75
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10073.95
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3983.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4222.85
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12065.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.27
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  7999981707

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:14.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.99
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000102079

Normal statistic for number of bits   :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.87
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:20.63

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:17.01
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 30  CouponCollector, r = 0          0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61177872.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:40.13

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:51.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:42.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4390
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7185
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.84
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.76
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.19
p-value of test                       :    0.9918

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.55
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:16.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.67
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.43
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.80
p-value of test                       :  5.8e-3

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.65
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.53
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  298.43
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.56
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1514.22
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6935.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.17
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.03
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:00.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.25
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4992.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:35.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46024
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870024
  j =  1                              :        399907955
  j =  2                              :            46018
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45831
p-value of test                       :    0.59


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869831
  j =  1                              :        399908343
  j =  2                              :            45821
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:13.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:48.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.92e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.98
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.02
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.45
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.64
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.94
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   14.33
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.04
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.14
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17626.35
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.54
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.88
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.54
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.06
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.57
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.02
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.90
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.44
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.50
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.91
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.14
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  469.42
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.88
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.98
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.57
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.01
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.74
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.78
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.70
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.70
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.77
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -1.39
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.34
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.24
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.15e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.38e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.20
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.38
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.51
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10070.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10028.57
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4817.99
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4951.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4247.93
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.42
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11833.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11865.97
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.33
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  8000100738

Normal statistic for number of bits   :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.48
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  8000016669

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:01.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.32

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.77
p-value of test                       :    0.04

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:59.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:10.48

 All tests were passed




Server wird beendet - Lösche Semaphor 62586896.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5490
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4224
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7483
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7424
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.23
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:52.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    3.43
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.65
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.17
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:33.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.49
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  201.68
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  417.52
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.05
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7068.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.10
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.81
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:46.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.37
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:39.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4979.03
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:17.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45592
p-value of test                       :    0.91


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869592
  j =  1                              :        399908820
  j =  2                              :            45584
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45836
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869836
  j =  1                              :        399908331
  j =  2                              :            45830
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:31.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:53.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 8.43e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.79e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.01
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.55
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.00
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  9.4e-4    *****

Anderson-Darling statistic = A2       :    5.52
p-value of test                       :  1.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   70.52
p-value of test                       :  2.0e-3

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:32.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.09
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:32.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.66
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17287.82
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   17.28
p-value of test                       :    0.9965


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.91
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.44
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.13
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:40.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.18
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.70
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.84
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.38
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.35
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.29
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.39
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  451.85
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.91
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.71
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.83
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.38
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.38
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.51
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.88
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.48
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  347.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.02
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.40
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.03
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.46
p-value of test                       :    0.93

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:09.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -2.15
p-value of test                       :    0.98

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.82e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-3
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:46.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.54
p-value of test                       :    0.9920

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.29
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.15
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  166.45
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:12.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9904.98
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:00.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.78
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:20.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4904.29
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4799.72
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4372.95
p-value of test                       :  2.8e-3

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4302.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11992.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11517.12
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.22
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999914126

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999886574

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:10.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    1.82
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:29.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.71
p-value of test                       :    0.24

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:20.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:10.95

 All tests were passed




Server wird beendet - Lösche Semaphor 42205192.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:55.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:48.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5345
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:45.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4477
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:34.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7134
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7065
p-value of test                       :    0.9985


-----------------------------------------------
CPU time used                    :  00:03:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     953
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.57
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     283
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:12.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.04
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.31
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.31
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:11.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.57
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:48.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1459.53
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6940.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.96
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.38
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.87
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5115.40
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:14.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908321
  j =  2                              :            45835
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46385
p-value of test                       :  9.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870385
  j =  1                              :        399907234
  j =  2                              :            46377
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:33.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:20.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:35.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.57e-4
p-value of test                       :  6.2e-3

Kolmogorov-Smirnov- statistic = D-    : 8.26e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.30e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:40.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.16
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.08
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.27
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 8.98e-3
p-value of test                       :    0.9903

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.07
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17281.96
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.34
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.73
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.22
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.25
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   33.51
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:00:37.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.22
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.78
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.95
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.64
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  533.07
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.64
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.26
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:46.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.71
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  572.48
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.42
p-value of test                       :  6.8e-3


-----------------------------------------------
CPU time used                    :  00:00:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  430.51
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  459.45
p-value of test                       :  4.9e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4917.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.04
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.34
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.43
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.88
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:27.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.65
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 5.87e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.53e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.05
p-value of test                       :    0.75

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:10.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.06
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:13.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10148.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.071
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.85
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.32
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4148.77
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3853.22
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11980.08
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11753.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.50
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999890900

Normal statistic for number of bits   :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.81
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  8000147673

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.77

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:28.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.08
p-value of test                       :    0.02

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:18.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:25.52

 All tests were passed




Server wird beendet - Lösche Semaphor 43024392.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:32.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5428
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:35.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4233
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7577
p-value of test                       :  1.3e-3


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.26
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.90
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.32
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.88
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.53
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.70
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.48
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  420.18
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1425.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7045.88
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   40.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.70
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.61
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5211.88
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:02.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45618
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869618
  j =  1                              :        399908766
  j =  2                              :            45614
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45915
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869915
  j =  1                              :        399908175
  j =  2                              :            45905
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9990    *****

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.26e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.32e-4
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.50
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.68
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.70
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.71
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.42
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:46.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.63
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:29.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.39
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  112.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17662.87
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.54
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.58
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.33
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.64
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.81
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.42
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.44
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.69
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.09
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.76
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.37
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.19
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.82
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.65
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.95
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.93
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.15
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.63
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.79
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.19
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.19
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.21
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.63
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:28.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.00
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   0.092
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.80e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 5.25e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.77e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.19
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.47
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.48
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9947.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4910.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.13
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4239.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.55
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11819.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.20
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999957218

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.11
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000096112

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    2.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -1.24
p-value of test                       :    0.89

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.96
p-value of test                       :    0.02

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:31.94
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 51  SampleProd, t = 16              0.9990 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44072968.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5548
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:36.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:03:54.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7431
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.91
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.06
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:11.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.43
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.35
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.11
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  463.68
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1565.13
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:02:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7103.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.51
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.31
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:08.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.20
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.09
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.91
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:01.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908335
  j =  2                              :            45831
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45802
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869802
  j =  1                              :        399908398
  j =  2                              :            45798
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:33.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.83
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.34e-4
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.83e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.97e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.95
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:22.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.99
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.82
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.23
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.37
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.07
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.32
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.89
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.23
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17535.52
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.78
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.68
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.18
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.64
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   60.46
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.84
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.96
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.53
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.27
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.85
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  184.73
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.39
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.40
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.84
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.28
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.76
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  426.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.52
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4926.31
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  383.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.74
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.16
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.39
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4959.80
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.29
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.47
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -1.04
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.82
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.17

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 8.49e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.85e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:42.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.21
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.83
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.21
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9886.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10108.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4917.84
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4109.08
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4268.96
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11704.43
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11593.09
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.97
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000004744

Normal statistic for number of bits   :   0.038
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.44
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000048805

Normal statistic for number of bits   :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:38.32

 All tests were passed




Server wird beendet - Lösche Semaphor 45121544.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:00.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5361
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7433
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7456
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.41
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.36
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     552
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.99
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     273
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    1.01
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    1.68
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.55
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.85
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.12
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.56
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.54
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.21
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  442.17
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.18
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7084.58
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.35
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.38
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.69
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.31
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:01.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45911
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869911
  j =  1                              :        399908181
  j =  2                              :            45905
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908083
  j =  2                              :            45954
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:34.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.88e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   55.23
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:55.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.76
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.51
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.07
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:46.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.29
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.72
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.65
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:18.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17671.41
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.56
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.98
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.68
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.36
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.76
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.01
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.69
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.15
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.59
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.36
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.55
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.15
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.61
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  191.82
p-value of test                       :  6.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.44
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.80
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  158.81
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.86
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.54
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4939.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.66
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.72
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.34
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4903.80
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.05
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.17
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.22
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.92
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    0.83
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.40e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.42e-3
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.11
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.09
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.02
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9981

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10033.81
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.81
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:03.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.066
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:31.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4786.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.47
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4161.67
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12135.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   80.83
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999803975

Normal statistic for number of bits   :   -1.55
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.73
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000042283

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :    1.19
p-value of test                       :    0.12

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    2.73
p-value of test                       :  3.5e-3

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    2.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:06.70

 All tests were passed




Server wird beendet - Lösche Semaphor 46170120.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:50.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5352
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:42.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7110
p-value of test                       :    0.9926


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.91
p-value of test                       :  9.9e-3

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.30
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     329
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    2.02
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     134
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.30
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.78
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.50
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.43
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:47.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1473.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.77
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:16.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.87
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:10.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.84
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4987.64
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:55.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45499
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869499
  j =  1                              :        399909005
  j =  2                              :            45493
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908300
  j =  2                              :            45847
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:32.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:49.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.21e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.31e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.95e-4
p-value of test                       :  1.9e-3

Kolmogorov-Smirnov- statistic = D-    : 4.07e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    5.87
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.55
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.54
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.00
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.85
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.10
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.33
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.62
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.66
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.76
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:39.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.36
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.32
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.90
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.17
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.50
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.91
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.96
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.17
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.10
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.64
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.15
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.09
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.90
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.61
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.92
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  453.09
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.27
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.12
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4992.30
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.61
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.19
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  344.64
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.45
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.91
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  230.27
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.24
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.66
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    0.88
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:02:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 6.26e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.10
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9845.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10105.58
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.33
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4955.33
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:57.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4124.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4167.10
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11968.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:32.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11881.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:33.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   66.37
p-value of test                       :    0.12


-----------------------------------------------
Total number of bits:  8000015733

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   78.21
p-value of test                       :    0.02


-----------------------------------------------
Total number of bits:  7999959564

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:06.30

 All tests were passed




Server wird beendet - Lösche Semaphor 47185928.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1295
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334415
  j =  1                              :        599997410
  j =  2                              :             1295
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5627
p-value of test                       :  2.8e-3


-----------------------------------------------
CPU time used                    :  00:04:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4291
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:11.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7375
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:07.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    3.09
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     954
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.20
p-value of test                       :    0.27

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.73
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:12.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.96
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.04
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.84
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.93
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.96
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.98
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   92.14
p-value of test                       :  9.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:25.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.11
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1464.87
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7036.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.34
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:17.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   78.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:03:15.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.02
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.84
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:41.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5113.06
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:27.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:01.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45643
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869643
  j =  1                              :        399908717
  j =  2                              :            45637
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45692
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869692
  j =  1                              :        399908617
  j =  2                              :            45690
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:32.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.42
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.61e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.11e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.05e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.97
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.19
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:42.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.06
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.77
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.75
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.74
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.57
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:00.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.79
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.49
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:50.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9915

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.61
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.00
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.21
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.36
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17565.64
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.10
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.92
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.90
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.94
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.38
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.38
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.31
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.53
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.85
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.13
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.46
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.19
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.55
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.32
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.57
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.75
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.59
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4852.05
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.19
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.08
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4945.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.89
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.79
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.12
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:02:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.49
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.078
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.18e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.71e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.80
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.84
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.32e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.0e-3

Anderson-Darling statistic = A2       :    4.43
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  255.96
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:02:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.71
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9965.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.74
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.09
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:35.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4816.67
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4842.93
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4198.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.04
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11790.80
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:31.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11815.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:34.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.17
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000083560

Normal statistic for number of bits   :    0.66
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  7999908711

Normal statistic for number of bits   :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:28.93
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 33  CouponCollector, r = 27         9.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 48234504.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5505
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7402
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:47.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.03
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.79
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    3.45
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     128
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.90
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.23
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.20
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:09.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.99
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.29
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  218.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.44
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.38
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6885.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.43
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:07.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    9.47
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.13
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5023.98
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:56.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908176
  j =  2                              :            45909
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45995
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869995
  j =  1                              :        399908015
  j =  2                              :            45985
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:29.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.41
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.65e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.68e-5
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    : 2.51e-4
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 7.34e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:38.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.29
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.61
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.05
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.23
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.74
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.75
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17088.21
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.03
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.49
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.88
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.61
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.24
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.87
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.63
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.88
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.79
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.40
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.48
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.03
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.16
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.33
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.84
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.17
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.89
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.30
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.46
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.15
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.05
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.20
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.10
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.05
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4972.88
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.70
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.50
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.23
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.23
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.20
p-value of test                       :    0.77


-----------------------------------------------
Normal statistic for number of jumps  :   -1.30
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.92e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 3.55e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.42e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.78
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.72
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10166.52
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9971.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:02.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.86
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:20.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4863.43
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.54
p-value of test                       :  1.4e-3

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5088.92
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.66
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4166.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11598.07
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.07
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  8000122107

Normal statistic for number of bits   :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.49
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000037243

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    2.02
p-value of test                       :    0.02

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.55

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.13
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :    1.91
p-value of test                       :    0.03

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:41.63

 All tests were passed




Server wird beendet - Lösche Semaphor 49610782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1500
p-value of test                       :  1.5e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334620
  j =  1                              :        599997000
  j =  2                              :             1500
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4157
p-value of test                       :    0.9969


-----------------------------------------------
CPU time used                    :  00:02:01.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4275
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7172
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7308
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     571
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    4.93
p-value of test                       :  3.1e-3

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.21
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.71
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.55
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.98
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.48
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.54
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.44
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.69
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.74
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.10
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.67
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  164.32
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5077.17
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:25.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:56.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45939
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869939
  j =  1                              :        399908127
  j =  2                              :            45929
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45932
p-value of test                       :    0.40


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869932
  j =  1                              :        399908142
  j =  2                              :            45920
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:32.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:20.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.97


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.8e-3

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.59e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.54
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.92
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.42
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.47
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17415.25
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.97
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.26
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.20
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.16
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.98
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.71
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.32
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.28
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   95.96
p-value of test                       :    0.9963


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.18
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.15
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.56
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.93
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.28
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.51
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.85
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.94
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4991.92
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.47
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.52
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.36
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.51
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  382.03
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.06
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:34.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.22
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.29
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:02:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.37
p-value of test                       :    0.92

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 8.08e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.14
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.94
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.51
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.4e-4    *****

Anderson-Darling statistic = A2       :    4.42
p-value of test                       :  5.7e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10155.61
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10159.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.77
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4915.62
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4071.95
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11678.23
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:35.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11939.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.13
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000059038

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.56
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  7999985451

Normal statistic for number of bits   :   -0.12
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  1.0e-2

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:18.92

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:09.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  4  CollisionOver, t = 2            1.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50528286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5437
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7413
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:04:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    1.44
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.27
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:19.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:16.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.60
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.06
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.48
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.00
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.40
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:12.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.68
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  270.99
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1407.89
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7022.09
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.08
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.40
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:08.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.50
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:00.46

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45966
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869966
  j =  1                              :        399908075
  j =  2                              :            45952
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45646
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869646
  j =  1                              :        399908709
  j =  2                              :            45644
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-3
p-value of test                       :    0.9979

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  6.8e-4    *****

Anderson-Darling statistic = A2       :    5.72
p-value of test                       :  1.4e-3


-----------------------------------------------
CPU time used                    :  00:02:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.41e-5
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.61
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.66
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.15
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.51
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.34
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.93
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.47
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.83
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.056
p-value of test                       :    0.9966

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.01
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.96
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17705.68
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.89
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.89
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.27
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.86
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.43
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.09
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.35
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.72
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.35
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.15
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.94
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.14
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.94
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.10
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   95.41
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.21
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.57
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.62
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.72
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.92
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.28
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5082.07
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.35
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.21
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.70
p-value of test                       :    0.12


-----------------------------------------------
Normal statistic for number of jumps  :   -0.66
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.28
p-value of test                       :    0.68


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.72

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.77
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.21
p-value of test                       :    0.73

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.88
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10068.41
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.070
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:04:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4860.39
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.52
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4018.63
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.20
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11611.73
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.47
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000015787

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.74
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  8000096277

Normal statistic for number of bits   :    0.76
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.57

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.92
p-value of test                       :    0.97

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:12.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.86

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.03

 All tests were passed




Server wird beendet - Lösche Semaphor 51609630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5348
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:42.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:08.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.30
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     332
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    2.94
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     137
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.85
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.72
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.44
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.05
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.25
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.71
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  280.33
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.12
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   18.83
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.80
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   40.83
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.06
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  149.96
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5081.08
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:13.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:56.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907898
  j =  2                              :            46048
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45697
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869697
  j =  1                              :        399908610
  j =  2                              :            45689
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.30e-3
p-value of test                       :    0.9916

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.94e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.29
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.79
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   35.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.46
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.00
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.98
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.46
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.40
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:17.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17115.00
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.25
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.79
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.62
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.03
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.71
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.69
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.04
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.50
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.44
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.80
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.38
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.66
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.88
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.60
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.31
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.04
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.81
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.63
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.33
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5009.69
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  323.10
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.30
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.89
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.02
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4951.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.19
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.36
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.36
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.58
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.73e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 7.52e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.86
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.68
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.64
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.41
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.54
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:04:20.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9952

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.85
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4779.68
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.37
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4226.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11986.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11752.15
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.25
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  8000066694

Normal statistic for number of bits   :    0.53
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   31.74
p-value of test                       :    0.9932


-----------------------------------------------
Total number of bits:  8000050662

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:14.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.43

 All tests were passed




Server wird beendet - Lösche Semaphor 52658206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5406
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:00.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7374
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7261
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7317
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7120
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:03:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7072
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:04:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.48
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.28
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    2.75
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.53
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:48.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.97
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.68
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.53
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.40
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.65
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.07
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.60
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.02
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1355.25
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7010.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.04
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.51
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:08.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.60
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.05
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4910.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:13.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:55.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45967
p-value of test                       :    0.34


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869967
  j =  1                              :        399908069
  j =  2                              :            45961
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46200
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870200
  j =  1                              :        399907604
  j =  2                              :            46192
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:30.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9951

-----------------------------------------------
CPU time used                    :  00:02:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 1.25e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.92
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.05
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.57
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.75
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.83
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 3.11e-3
p-value of test                       :    0.9968

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.35
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.33
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.50
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.37
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17299.66
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.12
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.81
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.77
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.38
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.69
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:37.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.14
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.53
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.03
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  164.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.46
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.77
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.31
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.44
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.35
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4901.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.24
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.02
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.01
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4821.83
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.00
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.19
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.63
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.17
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 7.66e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 3.91e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.34
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.70
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.10
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:07.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.59
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10300.11
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.27
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.036
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:04:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4777.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.4e-4    *****

Anderson-Darling statistic = A2       :    7.27
p-value of test                       :  2.7e-4    *****

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5240.33
p-value of test                       :  2.6e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3922.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4289.32
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11810.48
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11771.05
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:31.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.19
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000016756

Normal statistic for number of bits   :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.37
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000163996

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.84
p-value of test                       :    0.97

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.52

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:21.43
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 96  HammingIndep, L=30, r=27        2.6e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53608478.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5493
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4231
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7369
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7364
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7184
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.90
p-value of test                       :  3.3e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.36
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.40
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    2.16
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    1.32
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:17.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.99
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.48
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.64
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.28
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:20.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.34
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.12
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.49
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.67
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7002.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.75
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:08.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.09
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.97
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5199.18
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:04.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908766
  j =  2                              :            45611
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45898
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869898
  j =  1                              :        399908208
  j =  2                              :            45890
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:30.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.13e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.53e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 4.69e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 2.14e-4
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:44.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.87
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.09
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.24
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.38
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.89
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:46.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.85
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:27.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.72
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.67
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.14
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:54.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.15
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.64
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.68
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.25
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.80
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.33
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.52
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.12
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.96
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:38.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.45
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  460.73
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.94
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.71
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  102.52
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.73
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.36
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.24
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.26
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4800.11
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.36
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.27
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.61
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.35
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.83
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.65
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.33
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :    1.64
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 7.49e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.70e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.44
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.23
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   40.00
p-value of test                       :  4.5e-3



-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.24
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.72
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:06.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.97
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.86
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4753.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4349.04
p-value of test                       :  5.9e-3

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.73
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:33.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11689.68
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.48
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999850187

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.26
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  8000070585

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  7.1e-4    *****

Anderson-Darling statistic = A2       :    6.82
p-value of test                       :  4.4e-4    *****

Tests on the sum of all N observations
Standardized normal statistic         :    3.51
p-value of test                       :  2.2e-4    *****

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:15.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:38.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 105  AutoCor, d=1, r=27              2.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54624286.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5440
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7299
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     894
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.68
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:42.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.70
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.85
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   29.83
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.03
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.75
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.37
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1370.77
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7151.79
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.35
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.45
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.58
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:36.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4932.14
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45807
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869807
  j =  1                              :        399908387
  j =  2                              :            45805
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45666
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869666
  j =  1                              :        399908672
  j =  2                              :            45658
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.79
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:18.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.16e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.05e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 6.08e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.098
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.041
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.39
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.83
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.96
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.50
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.46
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.51
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.03
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17424.56
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.30
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.35
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.36
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.18
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.74
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   42.64
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.51
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.81
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.80
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.08
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.25
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.98
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.62
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.35
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.35
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.37
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.61
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.04
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.73
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.03
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:35.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.10
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.70
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.65
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    1.01
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.97
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.86
p-value of test                       :    0.03

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 7.08e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.90
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  255.12
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:02:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.47
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9894.15
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9962.94
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4925.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4996.03
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.43
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11846.08
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:31.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.10
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999963632

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   32.90
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  7999919325

Normal statistic for number of bits   :   -0.64
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :  -0.014
p-value of test                       :    0.51

Sample variance                       :    1.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.20
p-value of test                       :    0.58

Sample variance                       :    0.51
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.97
p-value of test                       :    0.17

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:39.03

 All tests were passed




Server wird beendet - Lösche Semaphor 55672862.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5498
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7439
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:12.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    5.54
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:02:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.55
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.49
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.52
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.77
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  401.29
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:48.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.93
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.16
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.71
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.56
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:09.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.50
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5193.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:01.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45917
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869917
  j =  1                              :        399908169
  j =  2                              :            45911
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45479
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869479
  j =  1                              :        399909046
  j =  2                              :            45471
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:35.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.37
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.56
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.35
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.53
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.36
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.11
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   10.47
p-value of test                       :  5.3e-3

-----------------------------------------------
CPU time used                    :  00:01:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17757.18
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.04
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.20
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.06
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.41
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   55.40
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.97
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.47
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.70
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.05
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.01
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.41
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   93.81
p-value of test                       :    0.9978


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.04
p-value of test                       :    0.9917


-----------------------------------------------
CPU time used                    :  00:00:43.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.24
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.18
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.53
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.15
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.53
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.18
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.04
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5093.94
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.61
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  342.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.04
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5161.43
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  403.18
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.66
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.44
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -1.46
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.07e-3
p-value of test                       :    0.9913

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :  -0.043
p-value of test                       :    0.52

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 4.19e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.68e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.97
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.87
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.85
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  249.99
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:02:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10190.10
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4730.95
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4688.65
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4246.30
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4079.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12021.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12100.50
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.10
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000108865

Normal statistic for number of bits   :    0.86
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.63
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000205045

Normal statistic for number of bits   :    1.62
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.89
p-value of test                       :    0.03

Sample variance                       :    1.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:47.47

 All tests were passed




Server wird beendet - Lösche Semaphor 56721438.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1323
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334443
  j =  1                              :        599997354
  j =  2                              :             1323
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5509
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4194
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4442
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.76
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    3.10
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    2.28
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    5.84
p-value of test                       :  1.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     358
p-value of test                       :  6.2e-4    *****

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:11.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.9907

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.46
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.23
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.68
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.92
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.72
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.12
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.14
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.57
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1443.02
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7192.47
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.84
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.88
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5177.55
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:12.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:06.28

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45811
p-value of test                       :    0.62


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869811
  j =  1                              :        399908382
  j =  2                              :            45803
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45988
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869988
  j =  1                              :        399908027
  j =  2                              :            45982
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.52
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:48.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :  2.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.46e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.59e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.81e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.87e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.15
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.080
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.01
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.06
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.64
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.88
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.82
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.98
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.02
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.77
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17196.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   56.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.42
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.65
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.23
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.75
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:38.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.26
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.49
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.82
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.66
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.72
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.91
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.78
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.83
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.29
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.20
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.22
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.77
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.79
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  222.02
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.50
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.60
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.85
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.46
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:34.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.91
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    1.04
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:02:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.03
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.57
p-value of test                       :  6.7e-4    *****

Anderson-Darling statistic = A2       :    4.36
p-value of test                       :  6.1e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.37
p-value of test                       :  8.9e-3

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 5.63e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.66e-3
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.56
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.22
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.65
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.63
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10069.89
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9967.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:18.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4746.63
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4712.57
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.20
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4053.32
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11550.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.78
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.92
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000080464

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.00
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999936329

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.89
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:22.88
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs NJumps, t = 9        6.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57737246.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:40.38

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1308
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334428
  j =  1                              :        599997384
  j =  2                              :             1308
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5443
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.89

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    5.94
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:49.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    2.66
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.04
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    5.23
p-value of test                       :  2.2e-3

-----------------------------------------------
CPU time used                    :  00:02:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.25
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.81
p-value of test                       :    0.47

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.16
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.43
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.67
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.39
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.52
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.33
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.44
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.93
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1378.31
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7291.46
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.60
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.70
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:06.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.15
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.14
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:35.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.52
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:04.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45535
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869535
  j =  1                              :        399908933
  j =  2                              :            45529
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908144
  j =  2                              :            45925
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.80e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.36e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.92e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 2.24e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.10
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  100.92
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.22
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.57
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.77
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.17
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.41
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.77
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17305.21
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.23
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.82
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.65
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.93
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.07
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.94
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.69
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.74
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.26
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.97
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.22
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.30
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.28
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.66
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  206.47
p-value of test                       :  9.2e-5    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.14
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.45
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.62
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.45
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.14
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.96
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.27
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5052.91
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.71
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  169.58
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.61
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.08
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.98
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.08

Sample variance                       :    2.15
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.18e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.26
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.21
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9739.44
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9991.06
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.50
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4778.59
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:51.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4877.55
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4196.56
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4067.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11948.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:31.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.63
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000107692

Normal statistic for number of bits   :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.69
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999919751

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:09.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.83
p-value of test                       :    0.80

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.92

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.45
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.98
p-value of test                       :    0.98

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:48.79
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 R (L=1000, r=20)    9.2e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 58753054.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:39.00

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5387
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:02.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4378
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:01.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:12.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7517
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     875
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:49.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     593
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.99


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:13.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.39
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.91
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:54.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.80
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.53
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.74
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.87
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.57
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  263.04
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1353.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7053.20
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.71
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.87
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:03:07.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.99
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.61
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4990.01
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:05.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46007
p-value of test                       :    0.28


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870007
  j =  1                              :        399907989
  j =  2                              :            46001
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45886
p-value of test                       :    0.49


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869886
  j =  1                              :        399908231
  j =  2                              :            45880
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:29.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.77
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:45.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.82e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 7.13e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.88
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:41.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.31
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.06
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.02
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.61
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.68
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.33
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:17.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.25
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.97
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   63.01
p-value of test                       :  3.5e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.59
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.15
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.34
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.79
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.75
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.24
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.29
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.67
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.58
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.29
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.07
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.45
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.06
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.46
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.12
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  524.66
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.85
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.37
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.92
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  358.18
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  185.01
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.41
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.54
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5155.49
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.74
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.94
p-value of test                       :    0.62


-----------------------------------------------
Normal statistic for number of jumps  :    1.34
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.02
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    1.68
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 4.72e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.24e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.83
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.44
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.39
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10288.45
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:13.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.07
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:53.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.97
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11784.33
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:30.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.95
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000035104

Normal statistic for number of bits   :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.54
p-value of test                       :    0.49


-----------------------------------------------
Total number of bits:  8000021670

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.69
p-value of test                       :    0.76

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:14.95

 All tests were passed




Server wird beendet - Lösche Semaphor 59801630.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:43.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7328
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:04:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.98
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.11
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    2.81
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.66
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.49
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:58.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:12.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.06
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.56
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.90
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  477.86
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:47.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1363.69
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7050.10
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.54
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   15.50
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:15.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.77
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:06.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.16
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:35.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4814.10
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:02.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45564
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869564
  j =  1                              :        399908877
  j =  2                              :            45554
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.90

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46228
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870228
  j =  1                              :        399907545
  j =  2                              :            46226
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:02:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.46e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.64
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  7.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.61e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 5.40e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.35
p-value of test                       :    0.9906

-----------------------------------------------
CPU time used                    :  00:01:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :  107.74
p-value of test                       :  1.2e-3

-----------------------------------------------
CPU time used                    :  00:00:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.01
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.96
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:55.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.89
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.94
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.24
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:27.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:17.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  131.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17240.85
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:53.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.84
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.02
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.65
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.88
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.60
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.20
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.66
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.60
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.75
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.64
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.92
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.19
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.04
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.88
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.18
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.43
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4950.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.67
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.50
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.47
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4929.27
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  381.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.58
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.54
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 3.99e-3
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.88
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.66
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.23
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.16
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.10
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10124.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9925.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.67
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4892.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.75
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:52.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3982.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11879.05
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:30.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.97
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.53
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999958442

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.40
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999886469

Normal statistic for number of bits   :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.54
p-value of test                       :    0.06

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.88
p-value of test                       :    0.19

Sample variance                       :    1.68
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:10.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:27.82
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 46  MaxOft AD, t = 8                0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60850206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1430
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334550
  j =  1                              :        599997140
  j =  2                              :             1430
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4404
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:12.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7281
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7177
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:09.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    2.82
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     843
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.63
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:19.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.76
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    3.30
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.85
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.18
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.15
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.33
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.73
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  383.87
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.91
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.14
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:14.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.60
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:06.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.28
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.32
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:35.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4818.34
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45634
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869634
  j =  1                              :        399908737
  j =  2                              :            45624
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45631
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869631
  j =  1                              :        399908744
  j =  2                              :            45619
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:29.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  8.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.98
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:04.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.27e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 4.95e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.87e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.75e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.083
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:40.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.41
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.34
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.17
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.50
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.61
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.8e-3

Kolmogorov-Smirnov- statistic = D-    : 8.24e-3
p-value of test                       :    0.9911

Anderson-Darling statistic = A2       :    3.58
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   20.29
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.65
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.47
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.50
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.81
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17717.62
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:00:52.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.25
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.55
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.52
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.29
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.15
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.95
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.90
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.69
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.09
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.83
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.59
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.56
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.45
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.19
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.45
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.45
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4996.71
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.54
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.94
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.21
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.14
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.86
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.19
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :   -2.72
p-value of test                       :    0.9968



-----------------------------------------------
CPU time used                    :  00:02:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.31
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   0.022
p-value of test                       :    0.49

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.93e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.11e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.79
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.68
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.49
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.29
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9856.93
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9863.38
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.68
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:04:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5078.05
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4824.92
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.91
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4029.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11788.37
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:30.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11929.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.35
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  8000155371

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.39
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000022369

Normal statistic for number of bits   :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.64

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:27.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    3.37
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    2.36
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:15.26

 All tests were passed




Server wird beendet - Lösche Semaphor 61866014.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9948


-----------------------------------------------
CPU time used                    :  00:00:46.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:01.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5458
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7487
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9995    *****

Test on the Nm values of W_{n,i}(mNP1):    1.16
p-value of test                       :    0.28

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.82
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    3.82
p-value of test                       :    0.01

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     672
p-value of test                       :  2.0e-3

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.80
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    2.25
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:11.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.57
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    4.36
p-value of test                       :  5.9e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     189
p-value of test                       :  1.2e-3

Stat. AD (mNP2)                       :    3.25
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.07
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.45
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.72
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:11.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.74
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.29
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  357.91
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:01:48.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1542.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7104.48
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.03
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.38
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:03:10.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.65
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:46.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5210.77
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:19.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45743
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869743
  j =  1                              :        399908516
  j =  2                              :            45739
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46225
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870225
  j =  1                              :        399907552
  j =  2                              :            46221
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:18.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:46.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.45e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 2.30e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.03e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.65
p-value of test                       :  4.1e-3

-----------------------------------------------
CPU time used                    :  00:01:47.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.78
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.10
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.93
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.39
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.48
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.76
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.22
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:32.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.39
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17514.04
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.08
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.21
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.12
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.60
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.76
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.03
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.63
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.65
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.47
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.65
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  535.68
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  166.68
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.33
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.38
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.66
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.32
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.55
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.83
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.01
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.96
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.46
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.71
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4881.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.17
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.74
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.44
p-value of test                       :    0.17


-----------------------------------------------
Normal statistic for number of jumps  :    1.69
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:02:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.95
p-value of test                       :    0.96


-----------------------------------------------
Normal statistic for number of jumps  :    0.49
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:14.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.01e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 8.26e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:47.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.28
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.81
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:10.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.31
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10003.80
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:59.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:04:22.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4687.84
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4804.20
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.30
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11384.16
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11703.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.79
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  8000007411

Normal statistic for number of bits   :   0.059
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   79.79
p-value of test                       :    0.01


-----------------------------------------------
Total number of bits:  7999987236

Normal statistic for number of bits   :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:09.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.012
p-value of test                       :    0.50

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.67
p-value of test                       :    0.75

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.34
p-value of test                       :    0.37

Sample variance                       :    1.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:21:07.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 22  ClosePairs mNP, t = 3           0.9995 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42237961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:40.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:18.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:32.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5515
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:49.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7208
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7377
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:11.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    1.09
p-value of test                       :    0.31

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     553
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.43
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.95
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.35
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.19
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.32
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.21
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  202.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.42
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1329.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.12
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   43.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.36
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5055.81
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:05.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908188
  j =  2                              :            45897
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45945
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869945
  j =  1                              :        399908114
  j =  2                              :            45937
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9918

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:31.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:20.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:52.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 8.22e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.66
p-value of test                       :  3.9e-3

-----------------------------------------------
CPU time used                    :  00:00:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.025
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:48.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.69
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.51
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.03
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:52.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.97
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:01.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.02
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   42.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  161.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17345.62
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.20
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.59
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:39.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.11
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.54
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.89
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.02
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.58
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.84
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.88
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.68
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.78
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  620.17
p-value of test                       :  1.9e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.90
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.85
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.81
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  311.40
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5140.00
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.31
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.73
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.01
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.89
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  333.80
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.99
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -1.34
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.84
p-value of test                       :    0.99


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.26
p-value of test                       :    0.10

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.21e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 8.84e-3
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.97e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 9.91e-3
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.11
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.76
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.8e-3

Anderson-Darling statistic = A2       :    3.28
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  248.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.91
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9813.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:02.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:33.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4173.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3908.79
p-value of test                       :    0.9900

-----------------------------------------------
CPU time used                    :  00:01:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11651.43
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:34.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11803.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.97
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999964931

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.08
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999922295

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:21.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :   0.029
p-value of test                       :    0.49

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:52.04
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 J (L=1000, r=20)    1.9e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 43155465.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:47.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:58.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:02.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1315
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334435
  j =  1                              :        599997370
  j =  2                              :             1315
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4465
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4286
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7264
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:05.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.21
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    1.81
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.94
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.05
p-value of test                       :    0.33


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    2.44
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     177
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.95
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.50
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.20
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.32
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.94
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.90
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1475.68
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:01.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7213.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.22
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.20
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:20.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.35
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.10
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:37.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5003.46
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:58.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46150
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870150
  j =  1                              :        399907703
  j =  2                              :            46144
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45568
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869568
  j =  1                              :        399908868
  j =  2                              :            45560
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:28.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:16.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.69e-3
p-value of test                       :    0.9937

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.01e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.20
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.07
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.33
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.41
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.64
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.86
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.53
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.04
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.90
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:09.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.9998    *****

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.46
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17375.14
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:54.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.16
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.78
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.88
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.26
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.00
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.15
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.81
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.01
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.23
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.67
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.30
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.14
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.24
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.84
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.09
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.24
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.66
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.93
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.86
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.48
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.17
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  155.96
p-value of test                       :    0.9907


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.27
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4965.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.42
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.55
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:28.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.29
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:28.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.97e-3
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    : 9.40e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.16
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.63
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.07
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9866.99
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.45
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:04:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4936.39
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4870.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:56.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.69
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.48
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11691.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11628.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.49
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000179821

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.88
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000156139

Normal statistic for number of bits   :    1.23
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.29
p-value of test                       :    0.61

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    2.42
p-value of test                       :  9.5e-3

-----------------------------------------------
CPU time used                    :  00:01:12.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:15.00

 All tests were passed




Server wird beendet - Lösche Semaphor 44957705.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:45.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:53.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5274
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7482
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:38.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4353
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:03:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7392
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7479
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:03:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.47
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:47.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.18
p-value of test                       :    0.9956

Stat. AD after spacings (mNP2-S)      :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.49
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     280
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    3.36
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:44.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.93
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.75
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.52
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.18
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.83
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.46
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.86
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1418.29
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7198.82
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.31
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.29
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:13.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.25
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.75
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4988.01
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:14.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:59.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46268
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870268
  j =  1                              :        399907467
  j =  2                              :            46262
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 2.19e-3
p-value of test                       :    0.9977

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9973


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:18.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:17.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.22e-4
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 7.58e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 2.21e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.66
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.57
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.59
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.82
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.84
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.48
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   53.65
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.68
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:29.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:08.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.29
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17362.88
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:54.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.22
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.73
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.68
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.17
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.64
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.09
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.36
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.25
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.94
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.27
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.60
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.47
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.05
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.90
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.92
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4990.55
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  355.97
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.21
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.52
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5271.14
p-value of test                       :  3.8e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.44
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.77
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.13
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.44
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.44
p-value of test                       :    0.93

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.75
p-value of test                       :    0.23

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.89e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9920

-----------------------------------------------
CPU time used                    :  00:00:46.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.06
p-value of test                       :    0.34

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.47
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.93
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.02
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9922.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:04:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4887.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4857.64
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.81
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4050.25
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11723.95
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.71
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:31.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.97
p-value of test                       :    0.48


-----------------------------------------------
Total number of bits:  7999746501

Normal statistic for number of bits   :   -2.00
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.86
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999939209

Normal statistic for number of bits   :   -0.48
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :  -0.032
p-value of test                       :    0.51

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:26.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:13.47

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:13.34

 All tests were passed




Server wird beendet - Lösche Semaphor 45842441.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:42.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5357
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4423
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:55.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4533
p-value of test                       :  1.6e-3


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.39
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     844
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.85

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     293
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:15.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.20
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    2.44
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.67
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.81
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:05.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.18
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.78
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.79
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.82
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  200.34
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  467.26
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1359.56
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7172.89
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:14.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9975

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.17
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:11.34

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   13.32
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4936.12
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:03:00.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45717
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869717
  j =  1                              :        399908568
  j =  2                              :            45713
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46001
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870001
  j =  1                              :        399908000
  j =  2                              :            45997
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.26
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.48e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.46e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.55e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.75
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:22.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:40.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.77
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.96
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.08
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.68
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.52
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.59
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.55
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.42
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.75
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.27
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.21
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   93.21
p-value of test                       :    0.9938

-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17495.00
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:00:53.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.67
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.20
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.76
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.52
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:37.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.82
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.83
p-value of test                       :    0.9959


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.41
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.23
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.46
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.69
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.06
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.67
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.38
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.80
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  547.32
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.09
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.50
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.95
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.27
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4916.48
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.90
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.18
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.24
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.65
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5064.89
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.41
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.78
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.38
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:28.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :  -0.092
p-value of test                       :    0.54

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.52e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.61e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.43
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.86
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.73
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.19
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9821.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9862.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:01.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.50
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4814.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4338.18
p-value of test                       :  8.1e-3

-----------------------------------------------
CPU time used                    :  00:01:26.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.87
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12004.48
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11940.11
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.92
p-value of test                       :    0.27


-----------------------------------------------
Total number of bits:  8000023692

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.36
p-value of test                       :    0.85


-----------------------------------------------
Total number of bits:  8000014851

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.052
p-value of test                       :    0.52

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:13.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.75
p-value of test                       :    0.04

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:16.54

 All tests were passed




Server wird beendet - Lösche Semaphor 46694409.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:52.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5480
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4307
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:01:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7488
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7206
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     914
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.89
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.60
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.99
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.25
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.16
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.44
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  196.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.42
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:48.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.11
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   71.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.30
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.53
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5179.75
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:13.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:05.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45712
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869712
  j =  1                              :        399908580
  j =  2                              :            45704
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45651
p-value of test                       :    0.86


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869651
  j =  1                              :        399908699
  j =  2                              :            45649
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:30.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:01:47.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:36.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.64e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.17e-4
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.22
p-value of test                       :  6.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.69
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.49
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.61
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:58.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.02
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.92
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.31
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   67.15
p-value of test                       :  4.6e-3

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.30
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.61
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17084.90
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.71
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.63
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.74
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.70
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.56
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.51
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.72
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   35.06
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.33
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.96
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.44
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.19
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.53
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.71
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.46
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.47
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.40
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.06
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.43
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.98
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.40
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.59
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.81
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.44
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.31
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.87
p-value of test                       :    0.97



-----------------------------------------------
CPU time used                    :  00:02:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.27
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.01
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.87
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9732.57
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10086.58
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      : 2.05e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.03
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:53.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4940.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:56.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:25.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.78
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12025.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:31.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.89
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.54
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000007708

Normal statistic for number of bits   :   0.061
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.73
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  7999957269

Normal statistic for number of bits   :   -0.34
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.28
p-value of test                       :  6.7e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.60
p-value of test                       :    0.9954

Sample variance                       :    0.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:59.17
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               6.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47644681.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:41.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:52.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5372
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:00.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7322
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:09.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     897
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.27
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.54
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     320
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.71
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.93
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.99
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.20
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.48
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.36
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.39
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.69
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  255.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.33
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1541.30
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:01.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7044.22
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:10.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:47.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.07
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.05
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:01.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46103
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870103
  j =  1                              :        399907798
  j =  2                              :            46095
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46467
p-value of test                       :  3.1e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870467
  j =  1                              :        399907068
  j =  2                              :            46463
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:31.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:19.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:39.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.87e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.05e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:49.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:53.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.07
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:52.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.05
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.34
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.75
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.85
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:52.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.74
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.95
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:19.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.91
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17242.23
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.70
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.20
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.21
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.19
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.05
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.98
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.66
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.98
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.68
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.99
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.36
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.58
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.39
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  576.02
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.61
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.66
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.13
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.66
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.29
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.07
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.83
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.66
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.54
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.50
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.74
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.26
p-value of test                       :    0.28


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.60
p-value of test                       :    0.74


-----------------------------------------------
Normal statistic for number of jumps  :   -0.59
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    0.25
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.71e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 9.56e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.39
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   18.44
p-value of test                       :    0.02

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:34.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.69
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9958.25
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:59.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9943.25
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:36.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.58
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4905.72
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:58.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.00
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4144.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:27.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11825.04
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:33.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11894.49
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.00
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000056095

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.82
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000142459

Normal statistic for number of bits   :    1.13
p-value of test                       :    0.13



-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.55
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.72
p-value of test                       :    0.96

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:46.59

 All tests were passed




Server wird beendet - Lösche Semaphor 48660489.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:40.28

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:50.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1467
p-value of test                       :  3.1e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334587
  j =  1                              :        599997066
  j =  2                              :             1467
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5340
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4433
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7175
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7335
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:00.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:04:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    1.72
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     903
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:48.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.24
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.50
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.20
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.63
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.53
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.61
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.28
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.94
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  474.46
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1413.66
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7135.45
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.26
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.77
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.23
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  112.01
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5013.62
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:02.65

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45778
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869778
  j =  1                              :        399908447
  j =  2                              :            45772
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45671
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869671
  j =  1                              :        399908666
  j =  2                              :            45655
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:30.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9937


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.74e-3
p-value of test                       :    0.9910

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:18.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :  2.9e-3

Anderson-Darling statistic = A2       :    3.30
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.79e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.59e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.97e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.34
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.27
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.63
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.20
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9940

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.51
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:27.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:27.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.84
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:18.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  133.57
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17412.18
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:00:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.16
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.49
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.16
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.28
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.83
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.46
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.91
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.87
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.49
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.57
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.44
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.12
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.32
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.34
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  528.15
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.92
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.68
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.11
p-value of test                       :    0.9904


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.62
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4888.60
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.09
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.11
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.75
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.25
p-value of test                       :    0.9956


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  317.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  160.65
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.65
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.00e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 4.25e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.35
p-value of test                       :    0.72

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.07
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.50
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9879.75
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.18
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5127.07
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4828.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4153.68
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3942.00
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11780.46
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11795.98
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.36
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  7999870779

Normal statistic for number of bits   :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.26
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999968930

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.48e-3
p-value of test                       :    0.9920

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -2.04
p-value of test                       :    0.98

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.51
p-value of test                       :    0.93

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:12.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.33
p-value of test                       :    0.09

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.23
p-value of test                       :    0.59

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:29.39

 All tests were passed




Server wird beendet - Lösche Semaphor 50003977.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:51.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1441
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334561
  j =  1                              :        599997118
  j =  2                              :             1441
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5335
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:55.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4476
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:40.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4294
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7275
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.94
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.44
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.07
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.16
p-value of test                       :    0.9973

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.07
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     322
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    3.47
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.79

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     131
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    1.25
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9931

-----------------------------------------------
CPU time used                    :  00:02:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.83
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:56.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.07
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.98
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.41
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.58
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.50
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.10
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  246.20
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.90
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1398.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.82
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:09.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.09
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.44
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5142.51
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45773
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869773
  j =  1                              :        399908457
  j =  2                              :            45767
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45868
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869868
  j =  1                              :        399908268
  j =  2                              :            45860
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.56e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.28e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.09
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.43
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.58
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.88
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.04
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.84
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.39
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.55
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:28.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.93
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  9.0e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17918.91
p-value of test                       :  4.7e-3



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.53
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.16
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.72
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.82
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.23
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.51
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.30
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.14
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  447.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  104.72
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.71
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.57
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.34
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  103.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.14
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.51
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.86
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4867.05
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.23
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.78
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.13
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5186.18
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.56
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.20
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:27.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.95
p-value of test                       :    0.83

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.58
p-value of test                       :    0.06

Sample variance                       :    0.50
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.77e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 5.71e-3
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.05
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.11
p-value of test                       :    0.42

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.05
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9722.95
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10251.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.056
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:04:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4732.45
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4009.80
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11808.57
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11996.40
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.43
p-value of test                       :    0.79


-----------------------------------------------
Total number of bits:  7999948317

Normal statistic for number of bits   :   -0.41
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:05.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.88
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000010372

Normal statistic for number of bits   :   0.082
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:07.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    2.65
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.63
p-value of test                       :    0.95

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9926

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:25.39

 All tests were passed




Server wird beendet - Lösche Semaphor 50954249.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:51.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5501
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4430
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:00.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7076
p-value of test                       :    0.9978


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:04:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    1.92
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.55
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.66
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     600
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.74
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    3.84
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.43
p-value of test                       :  5.6e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.76

Test on the Nm values of W_{n,i}(mNP1):    1.47
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    4.46
p-value of test                       :  5.2e-3

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    3.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:42.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.37
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.23
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.64
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.29
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:17.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.73
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.88
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.56
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:31.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  410.14
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:52.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.23
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7015.78
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:15.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.54
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:48.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.01
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.89
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:31.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:57.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908492
  j =  2                              :            45748
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45800
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869800
  j =  1                              :        399908403
  j =  2                              :            45794
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:32.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:52.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:21.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.35e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.29e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.63e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.83e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.28
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.63
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:50.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.98
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:03.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:17.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   65.34
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.78
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.62
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:29.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.21
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.84
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17677.17
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.21
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.02
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.31
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.88
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.13
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.35
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.11
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.83
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.96
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.89
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.26
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.49
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.92
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.77
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.06
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  332.89
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.24
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.18
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:36.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.71
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4877.41
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  470.60
p-value of test                       :  8.2e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.10
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.10
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.28
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.57
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.32
p-value of test                       :    0.37

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.28e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.79
p-value of test                       :    0.04

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.48e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.12e-3
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.72
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.55
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:38.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.27
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9844.88
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10106.20
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.11
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.068
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5107.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:55.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3998.51
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.86
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:33.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11577.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.13
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  7999961709

Normal statistic for number of bits   :   -0.30
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.88
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000053458

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:17.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   0.083
p-value of test                       :    0.47

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.57
p-value of test                       :    0.72

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:29.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    0.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:20.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:04.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 R (L=10000, r=15)   8.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52002825.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:53.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4293
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7214
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.33
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     841
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.77

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    1.37
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     629
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.58
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     324
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.78
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.89
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.30
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.04
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.40
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.24
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.68
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  389.68
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1376.48
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.46
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.97
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.60
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.33
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:02.48

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45918
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869918
  j =  1                              :        399908166
  j =  2                              :            45914
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46260
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870260
  j =  1                              :        399907483
  j =  2                              :            46254
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.11e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.84
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.06
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.24
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.11
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.84
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.25
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:29.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.67
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.94
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  156.95
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.17
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17861.69
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:00:54.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.98
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.70
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.05
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.06
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.40
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.27
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.87
p-value of test                       :    0.9940


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.88
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.39
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  518.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.07
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.37
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.48
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.69
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.15
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.10
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5011.65
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.84
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.72
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  333.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4909.65
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.79
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.07
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.96
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:27.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 3.04e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 4.30e-3
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.00
p-value of test                       :    0.20

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.47
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.48
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:02:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9848.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:00.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9927.05
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :  -0.053
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.46
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:04:15.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.95e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5070.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4740.67
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4054.59
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4098.53
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11584.95
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11738.07
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.32
p-value of test                       :    0.88


-----------------------------------------------
Total number of bits:  8000091072

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:05.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.46
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000096820

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9948

Tests on the sum of all N observations
Standardized normal statistic         :   0.033
p-value of test                       :    0.49

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:09.57

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:25.11

 All tests were passed




Server wird beendet - Lösche Semaphor 53346313.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:40.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1289
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334409
  j =  1                              :        599997422
  j =  2                              :             1289
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7429
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     941
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.62
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    2.68
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     655
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    1.01
p-value of test                       :    0.35

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    1.79
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.56
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.16
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:06.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.59
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    5.68
p-value of test                       :    0.9973

-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.01
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.24
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.92
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.11
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  269.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.04
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.70
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6894.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.13
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.42
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.64
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.17
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5056.33
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:54.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45833
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869833
  j =  1                              :        399908336
  j =  2                              :            45829
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45658
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869658
  j =  1                              :        399908685
  j =  2                              :            45656
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:18.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:47.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:36.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.90e-4
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.86e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 9.59e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:50.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.70
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.87
p-value of test                       :  6.3e-3

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.29
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   18.61
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.54
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.41
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.97
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.51
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.49
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.29
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.30
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.12
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.96
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.26
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.43
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.72
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.48
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.80
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  175.00
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.06
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  105.57
p-value of test                       :    0.9952


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.31
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.98
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.19
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.90
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4919.02
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  322.30
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.15
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.01
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.36
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.95
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.30
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.38
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :    0.28
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.25
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.13
p-value of test                       :    0.87

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.55e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.76e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 8.75e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.92
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.01
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.23
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:07.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.15
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9976.89
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.24
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:15.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:54.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4760.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4197.21
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3967.89
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11634.07
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:30.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:30.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.01
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000007351

Normal statistic for number of bits   :   0.058
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.65
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999963317

Normal statistic for number of bits   :   -0.29
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.15
p-value of test                       :    0.56

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.72
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.07
p-value of test                       :    0.98

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.12

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.61
p-value of test                       :    0.27

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:51.12

 All tests were passed




Server wird beendet - Lösche Semaphor 54362121.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:41.72

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1293
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334413
  j =  1                              :        599997414
  j =  2                              :             1293
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5450
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:50.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4314
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:20.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:20.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7288
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7459
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:05:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:05:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    1.34
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    2.87
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     277
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    2.64
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:45.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.89
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.89
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.08
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.85
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.19
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.13
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:32.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1402.14
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:02.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6989.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.46
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.28
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:47.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.33
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5097.25
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:27.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:00.30

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46265
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870265
  j =  1                              :        399907473
  j =  2                              :            46259
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45430
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869430
  j =  1                              :        399909144
  j =  2                              :            45422
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:30.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:25.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :  1.7e-3

Anderson-Darling statistic = A2       :    3.03
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:52.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:20.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 2.20e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.08e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.17e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.21
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:26.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:10.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.08
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.29
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.63
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   44.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   63.80
p-value of test                       :  9.8e-3

-----------------------------------------------
CPU time used                    :  00:01:11.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.99
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:28.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.77
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.22
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17750.87
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.18
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.06
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.06
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.97
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.07
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.26
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.92
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.59
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.48
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.11
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.31
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:44.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.01
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.81
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.46
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.49
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.28
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.52
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5211.94
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  437.98
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.65
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.34
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5235.50
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.00
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.68
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:35.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.58
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.02
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.77
p-value of test                       :    0.78

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -1.14
p-value of test                       :    0.87

Sample variance                       :    0.81
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.53e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 9.32e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.07
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.38
p-value of test                       :    0.40

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:35.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9997.98
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9895.62
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.61
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:04:32.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5086.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4049.72
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:27.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12007.31
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11666.30
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.31
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999892874

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.05
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000153802

Normal statistic for number of bits   :    1.22
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :   0.073
p-value of test                       :    0.47

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   0.040
p-value of test                       :    0.48

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:01.86

 All tests were passed




Server wird beendet - Lösche Semaphor 55443465.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1428
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334548
  j =  1                              :        599997144
  j =  2                              :             1428
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5463
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4279
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:10.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7217
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:02.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:09.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     858
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    2.68
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    3.04
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:15.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.23
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     284
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.24
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     158
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    3.43
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.78
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.69
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.71
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.96
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.38
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  257.58
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.84
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1377.28
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7129.53
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.18
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.16
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.59
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  126.60
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5100.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46015
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870015
  j =  1                              :        399907972
  j =  2                              :            46011
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46173
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870173
  j =  1                              :        399907659
  j =  2                              :            46163
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :  8.3e-3

Kolmogorov-Smirnov- statistic = D-    : 1.72e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    3.55
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9973


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.25e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 9.25e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.05e-4
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 2.06e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:46.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:50.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.65
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.37
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.05
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:47.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.95
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.54
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.00
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.59
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.14
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.36
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.26
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.85
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.72
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.38
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.15
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   44.75
p-value of test                       :  6.2e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.25
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.03
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.81
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.47
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.08
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.90
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.32
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.63
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.50
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.53
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.72
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5092.44
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.46
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  247.37
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.13
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.32
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4958.60
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.30
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.04
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.57
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.33
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :   -0.80
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    2.64
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:46.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.38e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 5.64e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.51
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.47
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  236.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:06.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9994.15
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.94
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:01.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.018
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:00.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:03:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4970.66
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:51.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.47
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.00
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11717.57
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12063.22
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.77
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999967481

Normal statistic for number of bits   :   -0.26
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.40
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  7999975326

Normal statistic for number of bits   :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:01:04.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.38
p-value of test                       :    0.35

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:06.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    2.53
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:03.56

 All tests were passed




Server wird beendet - Lösche Semaphor 56557577.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:48.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.49

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5414
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:42.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7265
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:01.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:11.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:11.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:02.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.27
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.28
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.36
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.42
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.02
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.97
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.85
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:09.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.03
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.85
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.91
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.36
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.29
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:49.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:02.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6963.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   42.10
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.66
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:07.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.43
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   94.85
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5214.09
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:58.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908256
  j =  2                              :            45869
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908118
  j =  2                              :            45938
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:30.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:47.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:19.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.17e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 2.36e-5
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.67
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.29
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.96
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.05
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:49.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.96
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.75
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.31
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.86
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.32
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:27.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    9.42
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:40.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9969

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17405.33
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.35
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.92
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   32.89
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.01
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.58
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.01
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.90
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.62
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.39
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  536.47
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.30
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.26
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.76
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.47
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.18
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.05
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.03
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4872.59
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  327.03
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.54
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.37
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.57
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4988.73
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.96
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.02
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :    1.39
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.30
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:26.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -0.99
p-value of test                       :    0.84

Sample variance                       :    0.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.03e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.79e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.39e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 6.58e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.39
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.54
p-value of test                       :    0.09

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.26
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.75
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9796.69
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:01.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5032.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.79
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4175.75
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11690.61
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11962.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.95
p-value of test                       :    0.71


-----------------------------------------------
Total number of bits:  8000050872

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.95
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  8000137647

Normal statistic for number of bits   :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.30

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:43.29

 All tests were passed




Server wird beendet - Lösche Semaphor 57606153.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:48.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.08

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5320
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4225
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4295
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     956
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    2.56
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.42
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.19
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.25
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.77
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    2.00
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    2.10
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     132
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.40
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.13
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.62
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.29
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.90
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.40
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6872.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.95
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:03:08.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.10
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.61
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:36.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4876.62
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:13.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:02:58.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46244
p-value of test                       :    0.04


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870244
  j =  1                              :        399907516
  j =  2                              :            46236
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45905
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869905
  j =  1                              :        399908193
  j =  2                              :            45899
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:29.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.00e-5
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:44.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   37.52
p-value of test                       :    0.9987

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.05
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.27
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.86
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   60.04
p-value of test                       :  9.7e-3

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.70
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.85
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:17.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.39
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.09
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17113.60
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.97
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   54.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   47.31
p-value of test                       :  4.5e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.71
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.78
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.86
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.59
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.84
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.08
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.60
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.42
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  101.15
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.38
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.03
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  477.38
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.67
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.73
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.90
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.76
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4783.41
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.62
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.70
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.26
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.07
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5048.16
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.07
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.85
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.79
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.19
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.28
p-value of test                       :    0.06


-----------------------------------------------
Normal statistic for number of jumps  :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:02:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.76e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 9.46e-3
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.91e-3
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.17
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.42
p-value of test                       :    0.24

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.53
p-value of test                       :  2.1e-3

Kolmogorov-Smirnov- statistic = D-    : 3.58e-3
p-value of test                       :    0.9963

Anderson-Darling statistic = A2       :    3.93
p-value of test                       :  9.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  153.78
p-value of test                       :    0.9935

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.60
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9993.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9693.80
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:51.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4800.67
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4089.48
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4075.66
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11688.28
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12168.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.82
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  8000057517

Normal statistic for number of bits   :    0.45
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.31
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000010498

Normal statistic for number of bits   :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.43
p-value of test                       :    0.67

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.85
p-value of test                       :    0.20

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:57.11

 All tests were passed




Server wird beendet - Lösche Semaphor 58621961.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:07.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1483
p-value of test                       :  7.8e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334603
  j =  1                              :        599997034
  j =  2                              :             1483
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.99

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5307
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:03:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4467
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:42.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:59.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4305
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7419
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7529
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:04:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.25
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     857
p-value of test                       :    0.92

Stat. AD (mNP2)                       :    1.91
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.52
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.18
p-value of test                       :    0.9945

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:14.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.18
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:47.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.21
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.59
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.47
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.97
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.46
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.43
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  237.65
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.00
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:52.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.04
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:03.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7117.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.66
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:03:07.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.55
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.48
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.73
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:01.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45960
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869960
  j =  1                              :        399908085
  j =  2                              :            45950
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45951
p-value of test                       :    0.37


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869951
  j =  1                              :        399908101
  j =  2                              :            45945
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:47.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.4e-3

Kolmogorov-Smirnov- statistic = D-    : 7.58e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    5.10
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.78e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 5.92e-5
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.89
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:51.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.11
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.14
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.22
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.72
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.39
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.56
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.54
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:17.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  121.41
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17620.31
p-value of test                       :    0.15



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.97
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.47
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.34
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.51
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.85
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.88
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.57
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.82
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.48
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.62
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  472.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.35
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.10
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.35
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.53
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.93
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.34
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.72
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.23
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.10
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.97
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.51
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.42
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.22
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5226.89
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.50
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.83
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.37
p-value of test                       :    0.58


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   26.11
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    1.96
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.60e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.33e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.47
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  232.15
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9990.64
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.77
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.48
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.030
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 1.82e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.93
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4999.43
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4083.80
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4287.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11575.72
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11705.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:29.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.51
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000024628

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.63
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000007528

Normal statistic for number of bits   :   0.060
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :    1.50
p-value of test                       :    0.07

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:46.19
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  6  CollisionOver, t = 3            7.8e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 59637769.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.58

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5447
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4393
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7242
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:41.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7236
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:04:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    1.22
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.72
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.74
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.95
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.94
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.14
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.15
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.09
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.14
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.84
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.36
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.36
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1506.55
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7016.52
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.66
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.42
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.68
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.05
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:36.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5005.35
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908683
  j =  2                              :            45651
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46058
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870058
  j =  1                              :        399907887
  j =  2                              :            46052
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:29.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:18.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.71
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.99e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.25e-5
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.94
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.035
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:52.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.56
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.38
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.78
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.03
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.84
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.24
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.03
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.98
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:17.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.29
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:39.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17579.95
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.86
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.70
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.35
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.14
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.80
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.43
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.08
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.03
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.92
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.67
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.46
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  461.65
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.44
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   65.55
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:45.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.87
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.59
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.41
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.51
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.24
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5089.49
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.55
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.33
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  354.38
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.13
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4934.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.96
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  215.65
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.11
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.78
p-value of test                       :    0.32


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:22.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -1.04
p-value of test                       :    0.85

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:08.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.70e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 7.85e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.98
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.65
p-value of test                       :    0.69

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.48
p-value of test                       :  6.7e-3

Anderson-Darling statistic = A2       :    5.05
p-value of test                       :  2.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  263.89
p-value of test                       :  1.6e-3

-----------------------------------------------
CPU time used                    :  00:02:04.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10101.54
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10049.51
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:04:10.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5062.80
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:53.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4838.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4063.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11534.27
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   69.63
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999852020

Normal statistic for number of bits   :   -1.17
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:04.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.52
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999851162

Normal statistic for number of bits   :   -1.18
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    1.22
p-value of test                       :    0.11

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:54.03

 All tests were passed




Server wird beendet - Lösche Semaphor 60686345.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:51.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5422
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:41.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:40.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4262
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:00.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:10.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     959
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    1.97
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.34
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:14.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.11
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:11.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.52
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.07
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  209.69
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.28
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:51.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1483.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7170.94
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.73
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.23
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:03:12.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.92
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.01
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5053.37
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:14.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:00.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45443
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869443
  j =  1                              :        399909117
  j =  2                              :            45437
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45735
p-value of test                       :    0.75


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869735
  j =  1                              :        399908534
  j =  2                              :            45727
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.22
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.01e+6
p-value of test                       :  8.8e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:31.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:19.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:51.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.39e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.76e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.68e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.06e-4
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.17
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:46.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.36
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.53
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.81
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.53
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.84
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:48.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.89
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.71
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.95
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.93
p-value of test                       :  3.0e-3

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:08.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.72
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17474.75
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.65
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   10.61
p-value of test                       :    0.9915


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.56
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.42
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.38
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.13
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.55
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.25
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.67
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.17
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.82
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.82
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.61
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   98.41
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.44
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.74
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.18
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.15
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.14
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  348.81
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.59
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.66
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :    0.55
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:02:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.82
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:02:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.10e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 3.70e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9980

-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.25
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9953.26
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:00.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.70
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:08.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.14
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:16.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4942.73
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4807.70
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4125.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4097.48
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11683.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:31.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.20
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.83
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000064837

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.06
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  8000006025

Normal statistic for number of bits   :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.25

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.23
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:12.90

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:07.42

 All tests were passed




Server wird beendet - Lösche Semaphor 61702153.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:39.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5383
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4354
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:40.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:42.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4368
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7285
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:04:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     905
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.56
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.56

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.26
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.91

Stat. AD after spacings (mNP2-S)      :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.99
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    1.46
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    2.79
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.61
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.87
p-value of test                       :    0.9967

-----------------------------------------------
CPU time used                    :  00:01:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.18
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.35
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.80
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.51
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.18
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.70
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.74
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1472.89
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.82
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.07
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.42
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.96
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.49
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4901.09
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:00.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46286
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870286
  j =  1                              :        399907430
  j =  2                              :            46282
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908509
  j =  2                              :            45738
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9968

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  7.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.63
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:47.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 1.40e-3
p-value of test                       :    0.9985

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:36.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.73e-5
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.70e-4
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    : 6.03e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:43.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.12
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.79
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.03
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.04
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.69
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.72
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.42
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:46.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.25
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.59
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17595.28
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:00:52.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.18
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.63
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.36
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.31
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.41
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.15
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.66
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.52
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.05
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.24
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.47
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.85
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.71
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.46
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.74
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.60
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.55
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.45
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:41.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.88
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.77
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5000.42
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.41
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:34.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.64
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.67
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5116.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.29
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.14
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:33.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.79
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.54
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :    1.84
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:16.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.57e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:41.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.08
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:19.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.99
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.92
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.89
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:54.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.07
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4795.00
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3957.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4076.02
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12066.46
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11571.80
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.17
p-value of test                       :    0.92


-----------------------------------------------
Total number of bits:  7999955991

Normal statistic for number of bits   :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:00:58.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.45
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  7999827549

Normal statistic for number of bits   :   -1.36
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:01:00.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.98
p-value of test                       :    0.02

Sample variance                       :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :   -1.49
p-value of test                       :    0.93

Sample variance                       :    1.07
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:58.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:01:47.39

 All tests were passed




Server wird beendet - Lösche Semaphor 62750729.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:01.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:15.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5456
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:36.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:34.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4381
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4372
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7284
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:01.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     885
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     555
p-value of test                       :    0.97

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.00
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:36.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.82
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.98
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.38
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.19
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.06
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.04
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.52
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  225.61
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:47.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1524.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6919.37
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.60
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   44.17
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.50e-3
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.57
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:10.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:44.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.08
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5254.76
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:19.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907860
  j =  2                              :            46067
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45528
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869528
  j =  1                              :        399908948
  j =  2                              :            45520
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:30.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.93


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:34.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.17e-4
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.35e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.33e-5
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:22.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.039
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :  -0.080
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.011
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.47
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   83.63
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.99
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.64
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.51
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.37
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.62
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.46e-3
p-value of test                       :    0.9943

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   62.08
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.92
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:32.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:40.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.14
p-value of test                       :    0.9991    *****

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17454.31
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.90
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.82
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   43.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.05
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.53
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:41.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.08
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.80
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.00
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   39.58
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:41.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.43
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.69
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.14
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.65
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.69
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.71
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.13
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  455.21
p-value of test                       :  7.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.94
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.40
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.71
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.13
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.93
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.82
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4915.04
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.10
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.26
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.58
p-value of test                       :    0.82


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:13.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.19
p-value of test                       :    0.29


-----------------------------------------------
Normal statistic for number of jumps  :   -0.91
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:14.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.47
p-value of test                       :    0.32

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.79e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 7.17e-3
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:47.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.50
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.37
p-value of test                       :    0.50

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:11.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.57
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.55
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9897.04
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:09.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.56
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4752.12
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4965.29
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4210.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12070.61
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11826.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.90
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000059980

Normal statistic for number of bits   :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.94
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  8000063694

Normal statistic for number of bits   :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:01:08.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.24
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:30.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:27.93

 All tests were passed




Server wird beendet - Lösche Semaphor 42270730.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:11.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:41.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:30.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:07.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:20.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5424
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:46.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7458
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4339
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:54.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7391
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.26
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.41
p-value of test                       :    0.02

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     866
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.33
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     607
p-value of test                       :    0.39

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:12.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    3.52
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     279
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:10.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.67
p-value of test                       :  4.6e-3

Test on the Nm values of W_{n,i}(mNP1):    2.53
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    3.10
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.82
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.25
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.69
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.35
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.93
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.57
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.78
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:47.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1452.61
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7324.88
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:49.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.71
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:03:09.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.01
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  160.63
p-value of test                       :  6.6e-3


-----------------------------------------------
CPU time used                    :  00:01:37.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5206.55
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:21.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46308
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870308
  j =  1                              :        399907388
  j =  2                              :            46300
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45625
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869625
  j =  1                              :        399908755
  j =  2                              :            45615
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:32.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.24


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:21.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:48.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:02.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:34.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.49e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.32e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.77e-4
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : 9.90e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.06
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.13
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.87
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.46
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   51.78
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.59
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.73
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  169.90
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.13
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.57
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.49
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.74
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.38
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.19
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:42.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.79
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.50
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   46.09
p-value of test                       :  6.3e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.59
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.89
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.62
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  445.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.53
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.69
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.47
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.31
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.00
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.65
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:43.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.41
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.83
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  433.17
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.07
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:33.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.02
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.91
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5079.78
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.03
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.57
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:32.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.81
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:02:14.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.72
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    1.80
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:16.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.93e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.23
p-value of test                       :    0.01

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.11e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:48.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.45e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 3.23e-3
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:46.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.09
p-value of test                       :    0.64

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.45
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  223.62
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:12.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.18
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10111.26
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.37e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10205.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:04:21.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5005.36
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:52.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.14
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4000.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3996.09
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11741.81
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.51
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:32.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.26
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999990197

Normal statistic for number of bits   :  -0.077
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:07.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   84.10
p-value of test                       :  5.4e-3


-----------------------------------------------
Total number of bits:  8000041785

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:10.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.67
p-value of test                       :    0.95

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:18.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:27.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:14.51

 All tests were passed




Server wird beendet - Lösche Semaphor 43384846.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:57.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:04.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1466
p-value of test                       :  3.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334586
  j =  1                              :        599997068
  j =  2                              :             1466
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5523
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:46.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4357
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:04:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:10.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.43
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.66
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     136
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    1.96
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.76
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.97
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.38
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.32
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.19
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.87
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  457.94
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1492.84
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7119.38
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:54.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.87
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:15.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:46.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  153.85
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.04
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:00.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45948
p-value of test                       :    0.38


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869948
  j =  1                              :        399908107
  j =  2                              :            45942
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45938
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869938
  j =  1                              :        399908128
  j =  2                              :            45930
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:33.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.96
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.40e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-4
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 1.69e-4
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.18
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.44
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.42
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   47.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.17
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.40
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.28
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.32
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.61
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:30.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.33
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17131.53
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.06
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.47
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.86
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.10
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.89
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.93
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.33
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   34.08
p-value of test                       :  8.2e-3


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.57
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  506.26
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.79
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.48
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.04
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  538.75
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.61
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   96.04
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.86
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5059.50
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  299.28
p-value of test                       :    0.9989


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.89
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.90
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.77
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4848.20
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.57
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.36
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.87
p-value of test                       :    0.54


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.56
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.18
p-value of test                       :    0.99

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :   -1.27
p-value of test                       :    0.90

Sample variance                       :    1.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.13e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-3
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.87
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.45
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.56
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:08.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.30
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9982.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10193.84
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:10.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.09
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4941.97
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.36
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4106.77
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11786.37
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.07
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:36.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.30
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999982418

Normal statistic for number of bits   :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.63
p-value of test                       :    0.64


-----------------------------------------------
Total number of bits:  8000152308

Normal statistic for number of bits   :    1.20
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:16.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    2.09
p-value of test                       :    0.02

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:17.12

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:39.34

 All tests were passed




Server wird beendet - Lösche Semaphor 44662798.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:31.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5419
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4434
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4440
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7323
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:57.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.77
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     957
p-value of test                       :    0.03

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.73
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.31
p-value of test                       :    0.93

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.13
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:43.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.57
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.49
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:59.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.33
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.24
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:09.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.66
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.69
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  215.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1454.92
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6974.54
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.72
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.54
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.07
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.68
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.20
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:16.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:03.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908238
  j =  2                              :            45878
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908298
  j =  2                              :            45848
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:31.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:20.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  2.5e-3

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:56.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.54e-4
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 5.57e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.58e-4
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.75
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.78
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:51.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.05
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.24
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.52
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.24
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.28
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.28
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17730.52
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:00:51.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.60
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.09
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   11.90
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.19
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.31
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.81
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.70
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.14
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   27.29
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.18
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  474.19
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.00
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.76
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.52
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.94
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.24
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.65
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.56
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5017.16
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  408.30
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.12
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.11
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5023.87
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  371.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.48
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.18
p-value of test                       :    0.11


-----------------------------------------------
Normal statistic for number of jumps  :    1.55
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.43
p-value of test                       :    0.67


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.14
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.36e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 8.30e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 6.10e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.60
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.69
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.62
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.56
p-value of test                       :  8.2e-4    *****

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10424.48
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9979.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.69
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.22
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:20.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5007.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4848.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.76
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4240.73
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.10
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11915.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.28
p-value of test                       :    0.82


-----------------------------------------------
Total number of bits:  8000021109

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.10
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  7999996686

Normal statistic for number of bits   :  -0.026
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.11

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.020
p-value of test                       :    0.51

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:13.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.17
p-value of test                       :    0.43

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:41.46

 All tests were passed




Server wird beendet - Lösche Semaphor 45481998.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:51.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1269
p-value of test                       :    0.9952

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334389
  j =  1                              :        599997462
  j =  2                              :             1269
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5489
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:51.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7315
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4266
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7519
p-value of test                       :  9.9e-3


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.88


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    2.16
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     940
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.17
p-value of test                       :    0.9961


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.53
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.65
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.75
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.96
p-value of test                       :    0.38

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.10
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.14
p-value of test                       :    0.9956

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.39
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   88.47
p-value of test                       :  2.1e-3

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  222.23
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.08
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1455.66
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7186.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.75
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.93
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:09.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.95
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:47.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.92
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:40.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5181.41
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:28.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.07

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46050
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870050
  j =  1                              :        399907903
  j =  2                              :            46044
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.05

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46121
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870121
  j =  1                              :        399907761
  j =  2                              :            46115
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:31.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 3.42e-3
p-value of test                       :    0.9963

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:57.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:39.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.10e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.99e-5
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:42.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.99
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.78
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.57
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.99
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.00
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:04.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   0.011
p-value of test                       :    0.9997    *****

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.19
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.37
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:43.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17701.15
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.88
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.21
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   29.19
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:38.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.32
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.94
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.36
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.63
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.99
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.71
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.06
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.96
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.42
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.53
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.20
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.72
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.56
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4984.79
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.14
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.75
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:37.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.45
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.90
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4890.77
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.27
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.80
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.53
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    0.58
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    1.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.25e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:46.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 3.62e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.64
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:18.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:18.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9963.95
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10083.03
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.096
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.079
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4682.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5023.96
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3936.36
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4041.07
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11319.92
p-value of test                       :    0.9996    *****

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11890.73
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:35.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.57
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  7999985886

Normal statistic for number of bits   :   -0.11
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.92
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999931952

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:13.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.93e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.84
p-value of test                       :    0.03

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:31.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   0.035
p-value of test                       :    0.49

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.12
p-value of test                       :    0.13

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:20.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:16.71
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 68  MatrixRank, L=1000, r=0         0.9997 
 99  HammingIndep, L=1200, r=0       0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 46497806.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5477
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:52.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4383
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:40.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:39.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4338
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4311
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:56.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7355
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:07.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.01
p-value of test                       :    0.35


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     900
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:48.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9943


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.86
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:15.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.89
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    3.06
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     168
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    3.67
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:40.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.16
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.26
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.66
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.88
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.21
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.88
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.39
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:51.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.22
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6986.51
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.67
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.91
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.94
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4945.66
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:01.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45974
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869974
  j =  1                              :        399908055
  j =  2                              :            45968
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45579
p-value of test                       :    0.92


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869579
  j =  1                              :        399908844
  j =  2                              :            45575
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:31.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:19.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:48.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.26e-5
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    : 2.36e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.41
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.95
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.87
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.63
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9970

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.02
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.94
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.48
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:41.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.63
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:54.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.79
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.56
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.47
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.52
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   47.51
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.09
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.40
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.43
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.74
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.80
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.51
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:46.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.84
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.83
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.80
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.79
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.37
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4858.19
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  236.03
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.24
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.63
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4885.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.03
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.11
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.11
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :    1.09
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.43
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.22e-3
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.96
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.67
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10038.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10080.02
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:09.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.53
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.058
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:04:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.39
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4736.93
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4038.50
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.01
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:32.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11875.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.28
p-value of test                       :    0.26


-----------------------------------------------
Total number of bits:  7999782609

Normal statistic for number of bits   :   -1.72
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.29
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999999284

Normal statistic for number of bits   : -5.66e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:08.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.05
p-value of test                       :    0.15

Sample variance                       :    0.35
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.60
p-value of test                       :    0.27

Sample variance                       :    0.47
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:12.59

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:11.37

 All tests were passed




Server wird beendet - Lösche Semaphor 47841294.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:42.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:51.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5446
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4253
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:04:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7464
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.54
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.01
p-value of test                       :  8.8e-3

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     922
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:46.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9951


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.97
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.35
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     302
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.18
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:02:40.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.90
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:57.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.89
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.80
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.56
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:01:12.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.66
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.83
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:24.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  253.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:27.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  473.57
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6965.00
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.12
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:15.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.38
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   85.44
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:15.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.98
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.73
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.07
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:17.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:56.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45982
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869982
  j =  1                              :        399908041
  j =  2                              :            45972
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45959
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869959
  j =  1                              :        399908085
  j =  2                              :            45953
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:20.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.91e-4
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 7.19e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.58e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.34e-4
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:40.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:42.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.85
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.99
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.30
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   59.89
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.40
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.99
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:47.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.09
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    7.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:28.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.74
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.53
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.83
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.30
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.25
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.36
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.37
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.96
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.65
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:37.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  120.88
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.16
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.76
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.41
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.98
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.79
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.57
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.69
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.80
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  444.30
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.68
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5100.39
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.35
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.70
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5051.08
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.89
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.66
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.79
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.44
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -1.45
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.77
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.46e-3
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:46.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 8.23e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:45.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.41
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.86
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:00.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.20
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4865.58
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4908.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4208.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:26.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4238.56
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11902.42
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11692.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.00
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  8000038752

Normal statistic for number of bits   :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.94
p-value of test                       :    0.59


-----------------------------------------------
Total number of bits:  7999883676

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   0.058
p-value of test                       :    0.48

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.93
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:26.68

 All tests were passed




Server wird beendet - Lösche Semaphor 48889870.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5486
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:55.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4309
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:42.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7171
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7136
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:12.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.07
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    2.03
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     849
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    2.53
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.36
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.46
p-value of test                       :    0.05


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.78
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:46.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.83
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:54.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.56
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.04
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.74
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.44
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.25
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.84
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  233.94
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1436.25
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:58.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7137.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.46
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.39
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:48.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.75
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:39.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5039.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908239
  j =  2                              :            45876
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45761
p-value of test                       :    0.71


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869761
  j =  1                              :        399908481
  j =  2                              :            45755
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :  7.5e-3

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.02


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:10.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:58.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:40.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.44e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 3.85e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.64e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.42
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.82
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.68
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.87
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.79
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.20
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.49
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.57
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.43
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.28
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.02
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.58
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.19
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.25
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:43.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17440.48
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.27
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.77
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.59
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.47
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.01
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.42
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.03
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.68
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.11
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.41
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.42
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.35
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.59
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:45.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.86
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  483.75
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.79
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.70
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.83
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  325.91
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4911.02
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.86
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  202.93
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.55
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.38
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5022.78
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.64
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.97
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.97
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -1.21
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.00
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:02:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.63e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 7.90e-3
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.59
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:29.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.73
p-value of test                       :    0.95

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.97
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:15.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  185.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:11.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9868.52
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9867.30
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:00.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:38.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4855.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4902.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:55.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.72
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.55
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11779.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:34.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   74.41
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999954758

Normal statistic for number of bits   :   -0.36
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.24
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999947000

Normal statistic for number of bits   :   -0.42
p-value of test                       :    0.66



-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:30.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:18.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:36.60

 All tests were passed




Server wird beendet - Lösche Semaphor 49840142.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1288
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334408
  j =  1                              :        599997424
  j =  2                              :             1288
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5265
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4380
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:42.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4302
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4274
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:07.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7154
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.53
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.56
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     945
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.74
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    1.87
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.64
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     627
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.58
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    0.19
p-value of test                       :    0.9918

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     299
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    2.17
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:14.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.59
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.23
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.09
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   20.21
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.60
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   31.42
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:22.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.24
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  249.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.10
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1448.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7322.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.52
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.63
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.20
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  134.79
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5110.70
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:10.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45899
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869899
  j =  1                              :        399908206
  j =  2                              :            45891
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.76

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45866
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869866
  j =  1                              :        399908270
  j =  2                              :            45862
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:30.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:18.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.98e-4
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 6.27e-5
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.78e-4
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.10
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.77
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.55
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.12
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.68
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.04
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.23
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.59
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.19
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.59
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.42
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.17
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:27.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.74
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:28.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.42
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:18.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.60
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.44
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:41.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17414.42
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:00:55.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.50
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.10
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.27
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:38.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.35
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.53
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.08
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.54
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.45
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.78
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.03
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.67
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.91
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.88
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.71
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  314.05
p-value of test                       :    0.9962


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.99
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4894.42
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.28
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.92
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.22
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.54
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.72
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  178.53
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.57
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :    1.29
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.49
p-value of test                       :    0.49


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.47
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.29e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.90e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:45.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.03
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.01
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10045.71
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9967

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10015.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:04:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4802.46
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4982.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:54.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.74
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.38
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11985.40
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:31.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11698.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.98
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999989624

Normal statistic for number of bits   :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  7999965645

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         : 1.00e-4
p-value of test                       :    0.50

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :    0.90
p-value of test                       :    0.19

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.21
p-value of test                       :    0.58

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:43.39

 All tests were passed




Server wird beendet - Lösche Semaphor 51150862.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:49.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1226
p-value of test                       : 1 -  7.5e-5    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334346
  j =  1                              :        599997548
  j =  2                              :             1226
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5364
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7567
p-value of test                       :  1.9e-3


-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4333
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4417
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:13.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:10.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7518
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.60
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.32
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    3.27
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.22
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    2.24
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     157
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    3.32
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:43.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.95
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.17
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   73.57
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.17
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.57
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:23.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.67
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  416.35
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1469.56
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7056.45
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:57.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.48
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   72.94
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:03:16.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.36
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:46.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.05
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:01:42.32

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:03:02.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46155
p-value of test                       :    0.10


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870155
  j =  1                              :        399907691
  j =  2                              :            46153
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45448
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869448
  j =  1                              :        399909108
  j =  2                              :            45440
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:02:21.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:52.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:12.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.52e-5
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    : 1.01e-4
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.26e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 7.57e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.85
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.18
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.39
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.16
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:58.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.48
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.70
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.47
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.88
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.01
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.69
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.45
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.79
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.64
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.78
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.76
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.47
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.28
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.30
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:38.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.96
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  180.57
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.45
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.10
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.23
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.39
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.83
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.17
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.42
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.44
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.54
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5199.22
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.47
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.93
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:36.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.40
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.34
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4952.78
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  449.46
p-value of test                       :  6.7e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  250.75
p-value of test                       :  8.6e-3


-----------------------------------------------
CPU time used                    :  00:00:36.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.10
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.15
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.40
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :    0.29
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.89

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 3.03e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.11e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.22
p-value of test                       :    0.10

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.19
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.92
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.4e-3

Anderson-Darling statistic = A2       :    3.25
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10142.74
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:58.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9974.67
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:04:33.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5056.14
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4958.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.80
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.95
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.73
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12077.50
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:39.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.37
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  8000032473

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.46
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000158011

Normal statistic for number of bits   :    1.25
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:01:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.5e-3

Anderson-Darling statistic = A2       :    4.12
p-value of test                       :  8.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :    2.42
p-value of test                       :  7.8e-3

Sample variance                       :    0.90
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:16.75

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:05.95
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14          1 -  7.5e-5
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52166670.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5436
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4283
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:57.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:04:00.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     932
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    2.26
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:47.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.27
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.88
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.02
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     133
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.63
p-value of test                       :    0.62

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:45.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.42
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.47
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.52
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.71
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.80
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.68
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.13
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  447.92
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1474.14
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:58.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.62
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   20.49
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:06.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.81
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.55
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:01:35.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.95
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:00.57

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908616
  j =  2                              :            45689
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45851
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869851
  j =  1                              :        399908303
  j =  2                              :            45841
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:30.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:35.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.10e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 9.22e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:22.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.094
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.10
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.22
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.66
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.66
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:44.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.40
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:29.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:29.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:19.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.62
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17262.82
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:00:54.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.70
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.28
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.85
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.68
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.00
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.05
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   17.03
p-value of test                       :    0.9954


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.46
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.34
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.18
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.84
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.71
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.11
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.04
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.58
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.77
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.27
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.02
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.69
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  394.25
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.46
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.34
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.82
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.64
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4839.36
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  405.58
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.93
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.80
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.66
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    0.51
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:25.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.22
p-value of test                       :    0.89

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.35
p-value of test                       :    0.09

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.67e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.66e-3
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 8.27e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.45
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.23
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.23
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:08.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.62
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9876.40
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.67
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.18
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:15.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.48
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4861.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:52.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4128.06
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11743.34
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:29.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:28.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.65
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000020278

Normal statistic for number of bits   :    0.16
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.22
p-value of test                       :    0.66


-----------------------------------------------
Total number of bits:  8000026587

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.67e-3
p-value of test                       :    0.9918

Anderson-Darling statistic = A2       :    2.11
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -2.01
p-value of test                       :    0.98

Sample variance                       :    1.22
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.048
p-value of test                       :    0.52

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    1.00
p-value of test                       :    0.16

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:05:43.14

 All tests were passed




Server wird beendet - Lösche Semaphor 53313550.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.42

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1301
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334421
  j =  1                              :        599997398
  j =  2                              :             1301
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5324
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4281
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:42.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:42.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4494
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:02:00.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7352
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7239
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:04:07.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.08
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    2.48
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    5.39
p-value of test                       :  2.1e-3

Test on the Nm values of W_{n,i}(mNP1):    7.14
p-value of test                       :  3.0e-4    *****

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     193
p-value of test                       :  4.2e-4    *****

Stat. AD (mNP2)                       :    1.43
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.98
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.81
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.71
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.27
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  236.10
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  470.99
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1383.39
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6877.88
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.14
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.93
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   91.20
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4983.41
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:12.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:54.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45660
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869660
  j =  1                              :        399908684
  j =  2                              :            45652
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.78

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46134
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870134
  j =  1                              :        399907735
  j =  2                              :            46128
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:30.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:18.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.51e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.20e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 1.18e-4
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.36e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.74e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.04
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.29
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.86
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.02
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.39
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.34
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.45
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.26
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   27.98
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.16
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.94
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.75
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.30
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:09.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  141.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17775.08
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:00:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.21
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.04
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.25
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.69
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:38.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.95
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.02
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.91
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.60
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.83
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.68
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.41
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.87
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.74
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.88
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.91
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.50
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4921.03
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  305.94
p-value of test                       :    0.9973


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.32
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.91
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.07
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5130.49
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.47
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.29
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.77
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.06
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :   -1.61
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :    1.14
p-value of test                       :    0.13

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.34
p-value of test                       :    0.09

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.01e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:46.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.65
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:27.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9842.31
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9835.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:02.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.62
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:04:16.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4984.64
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    4.80
p-value of test                       :  3.8e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4604.55
p-value of test                       :    0.9983

-----------------------------------------------
CPU time used                    :  00:01:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4118.37
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.88
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11891.29
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11991.37
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.42
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999964178

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.84
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000027433

Normal statistic for number of bits   :    0.22
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    0.11
p-value of test                       :    0.9994    *****

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :   -0.97
p-value of test                       :    0.83

Sample variance                       :    2.28
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 25  ClosePairs mNP1, t = 16         3.0e-4
 25  ClosePairs NJumps, t = 16       4.2e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 54296590.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:50.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1443
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334563
  j =  1                              :        599997114
  j =  2                              :             1443
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5474
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4246
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7182
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4429
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7450
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7325
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:03:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.46
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     895
p-value of test                       :    0.56

Stat. AD (mNP2)                       :    0.67
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    3.07
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.12
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     549
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    2.17
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.41
p-value of test                       :    0.20

Test on the Nm values of W_{n,i}(mNP1):    1.42
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.47
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.96
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.94
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.15
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.38
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:22.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.43
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.84
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.16
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.15
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:52.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1341.06
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7189.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.17
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:09.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.99
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  142.39
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:59.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46059
p-value of test                       :    0.20


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870059
  j =  1                              :        399907889
  j =  2                              :            46045
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45471
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869471
  j =  1                              :        399909066
  j =  2                              :            45455
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:17.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:46.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.19e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 2.85e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:40.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.13
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.97
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.71
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.19
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.65
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.28
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.06
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:48.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.19
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:28.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.83
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17199.89
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.32
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.78
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.39
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.97
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.03
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   52.90
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.32
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.49
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.86
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.53
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.54
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.87
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.45
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.68
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.55
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.29
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.32
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.11
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.70
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.48
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.03
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.39
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.75
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.84
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.39
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4860.41
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.64
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.33
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.19
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.35
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:02:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.76
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :    0.85
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.66

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    1.00
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.15e-4
p-value of test                       :    0.9953

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.32e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    : 9.04e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.46
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.31
p-value of test                       :    0.32

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.05
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.37
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.14
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9662.95
p-value of test                       :    0.9919

-----------------------------------------------
CPU time used                    :  00:00:59.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9940.36
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.068
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:14.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4822.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5002.68
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:54.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.52
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4168.47
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11764.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:32.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11724.09
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:31.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.10
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  7999922748

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.61
p-value of test                       :    0.87


-----------------------------------------------
Total number of bits:  7999912476

Normal statistic for number of bits   :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  6.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.34
p-value of test                       :    0.9903

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.047
p-value of test                       :    0.48

Sample variance                       :    0.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:30.15

 All tests were passed




Server wird beendet - Lösche Semaphor 55377934.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:40.53

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:51.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1478
p-value of test                       :  1.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334598
  j =  1                              :        599997044
  j =  2                              :             1478
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5289
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:52.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4410
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7318
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4365
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7156
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7224
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7347
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     935
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.33
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:48.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.24
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.14
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.24
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.28
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.27
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.60
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.54
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.83
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.37
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.70
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.20
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.46
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.66
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.33
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:48.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1426.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.29
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   46.27
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:13.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.73
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:03:08.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.83
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  143.57
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:36.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.38
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:13.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:00.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46148
p-value of test                       :    0.11


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870148
  j =  1                              :        399907707
  j =  2                              :            46142
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908434
  j =  2                              :            45780
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:17.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.60e-4
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 1.53e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.17
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.55
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.20
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.14
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.77
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.88
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.93
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:47.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.80
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.61
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.90
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.88
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17192.48
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.47
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.49
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.62
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.68
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.06
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.41
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.17
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.78
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  505.82
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.01
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.87
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.68
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :   98.47
p-value of test                       :    0.9991    *****


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  456.64
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.07
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  434.52
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.72
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5012.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.06
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.91
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.74
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4966.87
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.37
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  217.40
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.29
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:26.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.18
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :   -0.31
p-value of test                       :    0.62



-----------------------------------------------
CPU time used                    :  00:02:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    1.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.59
p-value of test                       :    0.72

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.48e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 7.79e-3
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 9.28e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.93
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.01
p-value of test                       :    0.54

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.54
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  190.86
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:02:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9916.91
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:59.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9966.20
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:04:12.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4891.66
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4900.48
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4051.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4232.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11814.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11603.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.67
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  8000202804

Normal statistic for number of bits   :    1.60
p-value of test                       :    0.05



-----------------------------------------------
CPU time used                    :  00:01:06.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.10
p-value of test                       :    0.80


-----------------------------------------------
Total number of bits:  8000010792

Normal statistic for number of bits   :   0.085
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9931

Tests on the sum of all N observations
Standardized normal statistic         :  -0.023
p-value of test                       :    0.51

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:10.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.56
p-value of test                       :    0.71

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:07.12
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 77  RandomWalk1 M (L=1000, r=20)    0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 56426510.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1279
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334399
  j =  1                              :        599997442
  j =  2                              :             1279
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5351
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:40.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4271
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4220
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:08.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7180
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.62
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     936
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.77
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    1.06
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    2.22
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     274
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    4.00
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:02:17.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.44
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.84

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     161
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.13
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.40
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:58.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.08
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:11.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.21
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  238.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  406.36
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1504.55
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6908.23
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:09.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.49
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.54
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5064.11
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:56.89

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908468
  j =  2                              :            45757
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45536
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869536
  j =  1                              :        399908931
  j =  2                              :            45530
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:29.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:17.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.39


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :  5.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    2.50
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:55.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.02e-4
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.20e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.21e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.39e-4
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:41.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.59
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.94
p-value of test                       :    0.9930

-----------------------------------------------
CPU time used                    :  00:00:56.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   86.43
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.43
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.92
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:46.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.82
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.86
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:29.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.01
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:29.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.49
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17215.14
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.75
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.01
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.68
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.34
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.71
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.10
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.19
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.62
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.45
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  177.22
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.85
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.26
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.14
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.29
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.49
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.42
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  109.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.84
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.47
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5036.44
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  214.05
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:35.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.22
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.05
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4904.29
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  141.54
p-value of test                       :    0.9994    *****


-----------------------------------------------
CPU time used                    :  00:00:35.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.49
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :  -0.086
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.17
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.76
p-value of test                       :    0.77

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.17
p-value of test                       :    0.12

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.02e-3
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.33e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.95e-3
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.91
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.52
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.03
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.34
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10252.51
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10067.40
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.03
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      : 1.45e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:04:18.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.94
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4853.83
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4158.71
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4260.18
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12097.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11540.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   36.30
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000002206

Normal statistic for number of bits   :   0.017
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.03
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999870179

Normal statistic for number of bits   :   -1.03
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:01:08.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.85
p-value of test                       :    0.97

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    2.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    1.90
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.50

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:38.15
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 79  RandomWalk1 C (L=10000, r=15)   0.9994 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 57376782.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:40.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7382
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:08.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7266
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:13.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.19
p-value of test                       :    0.9929


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.38
p-value of test                       :    0.06

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     899
p-value of test                       :    0.50

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:48.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    2.13
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.82
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    2.02
p-value of test                       :    0.09

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.36
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.93
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:57.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.19
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.81
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.44
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.78
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:12.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.99
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.23
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.53
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.90
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1494.55
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.02
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   35.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.25
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   82.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:18.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.85
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:46.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5031.45
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:03:01.67

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45628
p-value of test                       :    0.88


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869628
  j =  1                              :        399908745
  j =  2                              :            45626
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908184
  j =  2                              :            45905
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9961


-----------------------------------------------
CPU time used                    :  00:02:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.79
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:37.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 4.88e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.74e-4
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    : 6.67e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.093
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:43.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.80
p-value of test                       :    0.9974

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.53
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.97
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.52
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:50.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.25
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.52
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:50.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   24.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:03.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.08
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:28.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.25
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  115.26
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:44.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17598.66
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:00:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.50
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.41
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   32.13
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.55
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.15
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.95
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.19
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:37.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.38
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  197.30
p-value of test                       :  3.0e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.44
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.09
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.18
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.54
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.57
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.28
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.60
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.53
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.84
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5027.04
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.33
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  188.40
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  353.18
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.18
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4796.80
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  396.96
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.13
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.24
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    1.00
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:02:27.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   28.02
p-value of test                       :  5.5e-3


-----------------------------------------------
Normal statistic for number of jumps  :    0.18
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.02
p-value of test                       :    0.85

Sample variance                       :    0.33
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.90e-3
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 9.64e-3
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.59e-3
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.81
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.16
p-value of test                       :    0.25

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  231.00
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.51
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9878.32
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:07.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:04:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4829.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    3.47
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5107.00
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:00.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4145.70
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4081.81
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:28.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.53
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11760.11
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.11
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  7999940046

Normal statistic for number of bits   :   -0.47
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:01:04.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.40
p-value of test                       :    0.14


-----------------------------------------------
Total number of bits:  7999988841

Normal statistic for number of bits   :  -0.088
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :   0.055
p-value of test                       :    0.48

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.18
p-value of test                       :    0.57

Sample variance                       :    1.49
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.46

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:16.51

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:32.10

 All tests were passed




Server wird beendet - Lösche Semaphor 58359822.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:39.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5326
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4282
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4375
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7260
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7314
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.81

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    1.45
p-value of test                       :    0.19

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.96
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     309
p-value of test                       :    0.31

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.26
p-value of test                       :    0.24


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.11
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     147
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.75
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.22
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:05.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.96
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.62
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.76
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.68
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:21.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.86
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.64
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  433.72
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1435.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:02:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6875.49
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:49.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.37
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:14.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.44
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  145.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5169.73
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:13.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:01.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45777
p-value of test                       :    0.68


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869777
  j =  1                              :        399908450
  j =  2                              :            45769
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45909
p-value of test                       :    0.45


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869909
  j =  1                              :        399908188
  j =  2                              :            45897
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:18.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:44.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.08e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.62e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-4
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 1.81e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:24.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:39.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   80.03
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.02
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.29
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:56.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.57
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.69
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.57
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   27.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:46.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.40
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.33
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:30.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:28.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.41
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17254.90
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:00:53.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   19.57
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.97
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.15
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.11
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.24
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.08
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.21
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.31
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.81
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.47
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.08
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.88
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.48
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.60
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  117.48
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  163.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.49
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.54
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  428.75
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4982.16
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.16
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.06
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.80
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.59
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4948.94
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.53
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.43
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.75
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   0.043
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 6.89e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.04e-3
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.81
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.59
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.4e-3

Anderson-Darling statistic = A2       :    3.64
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  246.01
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  203.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9969.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9764.54
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4845.14
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4989.31
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4113.31
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4152.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11518.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:32.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11499.57
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.65
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000029911

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   75.30
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999891872

Normal statistic for number of bits   :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -0.53
p-value of test                       :    0.70

Sample variance                       :    1.72
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.37
p-value of test                       :    0.36

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:14.25

 All tests were passed




Server wird beendet - Lösche Semaphor 59441166.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.07

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5494
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:53.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:43.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4289
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4249
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:09.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:13.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.66
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     919
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     574
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.90


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.87
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     316
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.40
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.74
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:02:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.10
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.56
p-value of test                       :    0.16

Test on the Nm values of W_{n,i}(mNP1):    2.06
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     148
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.28
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.55
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:02.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.61
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:11.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.63
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:13.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.20
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.24
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.62
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1361.35
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6988.38
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.50
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:17.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.85
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:18.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.85
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  132.38
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:43.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5057.51
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:24.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:56.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46463
p-value of test                       :  3.3e-3


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870463
  j =  1                              :        399907076
  j =  2                              :            46459
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45536
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869536
  j =  1                              :        399908928
  j =  2                              :            45536
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :  8.1e-3

Kolmogorov-Smirnov- statistic = D-    : 2.56e-3
p-value of test                       :    0.9972

Anderson-Darling statistic = A2       :    3.99
p-value of test                       :  8.9e-3


-----------------------------------------------
CPU time used                    :  00:02:33.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:52.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:56.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :  5.9e-3

Anderson-Darling statistic = A2       :    4.23
p-value of test                       :  6.9e-3

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-5
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    : 2.62e-4
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.08e-4
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:24.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.69
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:41.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:41.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.78
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.71
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.63
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   20.52
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.05
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.77
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.92
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.36
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.20
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.07
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:17.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.78
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.25
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.19
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.19
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.33
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.60
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.50
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.82
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.98
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.61
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.49
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.19
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  168.50
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.92
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.81
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.05
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.12
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.03
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  464.26
p-value of test                       :  3.1e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.31
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.02
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:36.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.77
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.77
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5208.89
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  359.98
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  175.19
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.53
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.22
p-value of test                       :    0.18


-----------------------------------------------
Normal statistic for number of jumps  :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    1.59
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.39e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 6.57e-3
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   19.06
p-value of test                       :    0.01

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.87
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:00.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10007.05
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:04:28.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4709.58
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4964.58
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4164.86
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.96
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:28.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11745.36
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11896.82
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   91.63
p-value of test                       :  1.1e-3


-----------------------------------------------
Total number of bits:  7999863294

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.04
p-value of test                       :    0.51


-----------------------------------------------
Total number of bits:  7999927191

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.42

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.074
p-value of test                       :    0.47

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:15.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:52.95

 All tests were passed




Server wird beendet - Lösche Semaphor 60424206.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:40.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5358
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4411
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:41.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:41.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4330
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4290
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7356
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7304
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:00.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.93
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     609
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    2.00
p-value of test                       :    0.09

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     260
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.13
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.41
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.17
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:11.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.69
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.80
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.35
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.82
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  262.76
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  371.59
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1395.09
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.89
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:03:10.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.50
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.03
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:02.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45875
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869875
  j =  1                              :        399908253
  j =  2                              :            45869
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45987
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869987
  j =  1                              :        399908031
  j =  2                              :            45977
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:19.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:07.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:35.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.18e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.86e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 1.67e-4
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.04
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.51
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:23.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.78
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.21
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:56.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.96
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.97
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:49.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.84
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.22
p-value of test                       :  7.4e-3

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   40.24
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.11
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:04.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:29.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:29.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.12
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17510.53
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:00:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.72
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.36
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.93
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.61
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.05
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.99
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.12
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.99
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.09
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.63
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  566.90
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.19
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.16
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.05
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.63
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.79
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.30
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.30
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  359.00
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.33
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.15
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.15
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.24
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.87
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5063.62
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.56
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.89
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:34.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.56
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -1.96
p-value of test                       :    0.98



-----------------------------------------------
CPU time used                    :  00:02:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.92
p-value of test                       :    0.20


-----------------------------------------------
Normal statistic for number of jumps  :    0.79
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.74
p-value of test                       :    0.96

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.13e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 6.02e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.56
p-value of test                       :    0.58

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.49
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:26.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  178.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:07.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  171.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:07.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10211.53
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.92
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:05.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.28
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5017.86
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.51
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4218.67
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12079.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.72
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.81
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  7999905246

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.87
p-value of test                       :    0.60


-----------------------------------------------
Total number of bits:  8000024349

Normal statistic for number of bits   :    0.19
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :    0.20
p-value of test                       :    0.42

Sample variance                       :    0.73
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    3.32
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -2.05
p-value of test                       :    0.98

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:12.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.81
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :  -0.028
p-value of test                       :    0.51

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:10.76

 All tests were passed




Server wird beendet - Lösche Semaphor 61538318.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1409
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334529
  j =  1                              :        599997182
  j =  2                              :             1409
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5393
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4320
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:41.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:42.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7399
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7526
p-value of test                       :  7.9e-3


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.74


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.03
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     924
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:48.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    1.79
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     175
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    3.67
p-value of test                       :    0.01

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   15.78
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:55.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.82
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.80
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.82
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.18
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.05
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.35
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  229.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  464.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:48.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1421.41
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6925.83
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.12
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:14.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.76
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:07.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.90
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.67
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4930.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:12.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:00.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45698
p-value of test                       :    0.80


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869698
  j =  1                              :        399908607
  j =  2                              :            45692
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45277
p-value of test                       :    0.9976


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869277
  j =  1                              :        399909450
  j =  2                              :            45269
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:29.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.82
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.11e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.64e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.24e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 8.59e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.32
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.40
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:38.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.40
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:49.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.24
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.75
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.40
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.44
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:45.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.87
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.06
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.87
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.31
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:26.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.010
p-value of test                       :    0.9949

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.99
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17380.20
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.22
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.31
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.03
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:38.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.10
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.03
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.47
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.04
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.91
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.93
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.66
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.35
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:44.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.27
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.79
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.52
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.47
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  107.12
p-value of test                       :  7.1e-3


-----------------------------------------------
CPU time used                    :  00:00:43.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.43
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.94
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5060.86
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.52
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.80
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.94
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  338.37
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.07
p-value of test                       :    0.61


-----------------------------------------------
Normal statistic for number of jumps  :   0.025
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:02:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.05
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.65e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.04e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.86e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 7.45e-3
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.20
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.92
p-value of test                       :    0.21

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.01
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9955.92
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9931.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:56.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.87
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.20
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:03:34.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:46.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  7.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    3.06
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4713.16
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3974.42
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.96
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11721.12
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.25
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000009466

Normal statistic for number of bits   :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.76
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000076207

Normal statistic for number of bits   :    0.60
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:16.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.42
p-value of test                       :    0.34

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:18.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:03:29.42

 All tests were passed




Server wird beendet - Lösche Semaphor 62521358.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:01.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:38.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1528
p-value of test                       :  7.1e-6    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334648
  j =  1                              :        599996944
  j =  2                              :             1528
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1278
p-value of test                       :    0.9904

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334398
  j =  1                              :        599997444
  j =  2                              :             1278
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:46.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5404
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4252
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7210
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:37.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:57.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:06.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.72
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.71

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.22
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.64
p-value of test                       :    0.61

Test on the Nm values of W_{n,i}(mNP1):    3.47
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     561
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:13.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.29
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.49
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:36.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.99
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:56.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.33
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.01
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.05
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.66
p-value of test                       :    0.9905

-----------------------------------------------
CPU time used                    :  00:01:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.52
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.27
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.09
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  242.91
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:30.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  424.04
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1467.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6879.64
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.58
p-value of test                       :  4.4e-4    *****

Anderson-Darling statistic = A2       :    5.73
p-value of test                       :  1.4e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.46
p-value of test                       :  4.5e-3

-----------------------------------------------
CPU time used                    :  00:03:16.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.77
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  120.79
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:42.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5247.20
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:24.34

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45350
p-value of test                       :    0.9933


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869350
  j =  1                              :        399909305
  j =  2                              :            45340
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:10.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45891
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869891
  j =  1                              :        399908221
  j =  2                              :            45885
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:20.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.37


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:01:48.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.01e-5
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.48
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:53.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.88
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.50
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.95
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:53.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.04
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.83
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:54.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9903

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.55
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.90
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.06
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:33.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.92
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.080
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17387.38
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.80
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.60
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.92
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.62
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.40
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.73
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.79
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.75
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.20
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.77
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.57
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.70
p-value of test                       :  4.4e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.93
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.67
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:40.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.53
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.74
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.82
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.62
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.89
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:41.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.97
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.59
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5103.34
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  387.99
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.58
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.31
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.94
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5163.08
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.07
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  228.45
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.41
p-value of test                       :    0.41


-----------------------------------------------
Normal statistic for number of jumps  :   0.083
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:27.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.74
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -2.32
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:02:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -1.21
p-value of test                       :    0.89

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.74

Sample variance                       :    0.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.35e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:48.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.49e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 9.25e-3
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.90
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:29.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.95
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  168.53
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.19
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9779.06
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.14
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.38
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.37
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:04:29.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4774.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:56.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3994.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4060.13
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11936.57
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:34.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11576.32
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.45
p-value of test                       :    0.38


-----------------------------------------------
Total number of bits:  8000005746

Normal statistic for number of bits   :   0.045
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:09.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.76
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  7999969254

Normal statistic for number of bits   :   -0.24
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.70
p-value of test                       :    0.76

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.60
p-value of test                       :    0.73

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:23.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    0.93
p-value of test                       :    0.18

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:12.54

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:22:59.03
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           7.1e-6
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42303499.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:16.82

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:19.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1424
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334544
  j =  1                              :        599997152
  j =  2                              :             1424
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:28.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1319
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334439
  j =  1                              :        599997362
  j =  2                              :             1319
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1258
p-value of test                       :    0.9981

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334378
  j =  1                              :        599997484
  j =  2                              :             1258
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:40.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:59.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5510
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4386
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:39.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4418
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7153
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7181
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:04:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    4.36
p-value of test                       :  5.9e-3


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.08
p-value of test                       :    0.32

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     934
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    3.96
p-value of test                       :  9.1e-3

Stat. AD after spacings (mNP2-S)      :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.41
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     598
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.88
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:17.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    2.77
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:02:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.71
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.13
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:59.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.93
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:11.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   79.20
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.40
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.94
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.05
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  397.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:49.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1345.56
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7144.46
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:55.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.38
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   50.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:03:17.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.83
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  109.93
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.15
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:03.36

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45603
p-value of test                       :    0.90


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869603
  j =  1                              :        399908795
  j =  2                              :            45601
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.77

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46093
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870093
  j =  1                              :        399907815
  j =  2                              :            46091
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.82


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 8.69e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:47.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.027
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.43e-4
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    : 2.79e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.55e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.32e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.09
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   95.61
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.03
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.21
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:51.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   63.18
p-value of test                       :  4.7e-3

-----------------------------------------------
CPU time used                    :  00:00:59.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.10
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.75
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.15
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.45
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:59.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.59
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:30.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.34
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  109.17
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  5.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.04
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17006.61
p-value of test                       :    0.99



-----------------------------------------------
CPU time used                    :  00:00:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.62
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.91
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.67
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.07
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.28
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.90
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.33
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.08
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.41
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.03
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  496.62
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.49
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   55.31
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.12
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.37
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.30
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.15
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:46.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.69
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.39
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4754.94
p-value of test                       :    0.9935


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.21
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.49
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.87
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.66
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.82
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.02
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.76
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:37.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.80
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :  -0.060
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:28.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.59
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :   -1.24
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:07.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.70
p-value of test                       :    0.68

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.48
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  227.83
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    3.00
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  252.91
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:02:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9840.99
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9906.39
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.41
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:10.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5065.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.76
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3943.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4178.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11675.89
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:33.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11792.80
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.91
p-value of test                       :    0.74


-----------------------------------------------
Total number of bits:  8000070273

Normal statistic for number of bits   :    0.56
p-value of test                       :    0.29



-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.23
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000047941

Normal statistic for number of bits   :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    0.99
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:21.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :    0.12
p-value of test                       :    0.45

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.050
p-value of test                       :    0.48

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.43
p-value of test                       :    0.08

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:13.30

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:16.14

 All tests were passed




Server wird beendet - Lösche Semaphor 43843595.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:30.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1487
p-value of test                       :  5.4e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334607
  j =  1                              :        599997026
  j =  2                              :             1487
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1472
p-value of test                       :  2.0e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334592
  j =  1                              :        599997056
  j =  2                              :             1472
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5442
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:53.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4284
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4215
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:00.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7454
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7218
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:10.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7334
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.63
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     882
p-value of test                       :    0.72

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.31
p-value of test                       :    0.93


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.16
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.42
p-value of test                       :    0.83

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     586
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.23
p-value of test                       :    0.98


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.91
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.39
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    2.57
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.96
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.98
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.94
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.82
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.51
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.04
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.73
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:29.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.01
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1420.67
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:02.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6860.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.73
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.95
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.22
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:48.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   99.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.63
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:29.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:57.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45825
p-value of test                       :    0.60


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869825
  j =  1                              :        399908353
  j =  2                              :            45819
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.69

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45688
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869688
  j =  1                              :        399908626
  j =  2                              :            45684
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:23.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:01:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:10.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.89e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.73e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.85
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.22e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.45e-4
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.45
p-value of test                       :  7.1e-3

-----------------------------------------------
CPU time used                    :  00:00:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.25
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.076
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:52.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:51.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.87
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.65
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.14
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:52.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.44
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   38.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.98
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.88
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.56
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:27.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.94
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:30.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.91
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.65
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17182.44
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   57.01
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.96
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.86
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   28.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:38.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.66
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.67
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.94
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.20
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.07
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:38.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  116.38
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.68
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.11
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  124.00
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.92
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.12
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.71
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  504.64
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.65
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.71
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.14
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.58
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5085.32
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  331.54
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.43
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.28
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  435.51
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.60
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  418.40
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  180.30
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:35.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.00
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :    0.32
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   24.32
p-value of test                       :    0.02


-----------------------------------------------
Normal statistic for number of jumps  :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:02:25.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.81
p-value of test                       :    0.04

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:09.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.37e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 2.98e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.40
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:34.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.58
p-value of test                       :    0.38

-----------------------------------------------
Global longest run of 1               :   38.00
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:01:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.63
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:02:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10012.91
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:59.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9941.91
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:11.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.37
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:04:42.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4894.28
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:53.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5093.63
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:54.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4149.44
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4233.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11849.71
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11715.74
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.22
p-value of test                       :    0.73


-----------------------------------------------
Total number of bits:  8000180772

Normal statistic for number of bits   :    1.43
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.21
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000182935

Normal statistic for number of bits   :    1.45
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    1.18
p-value of test                       :    0.12

Sample variance                       :    0.79
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:06.29
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  9  CollisionOver, t = 14           5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 44826635.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:41.97

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:51.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5407
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:50.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4278
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:01:39.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4362
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:59.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7278
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:02.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7338
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.63
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.54

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     946
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.95
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:47.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.23
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     588
p-value of test                       :    0.68

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.64
p-value of test                       :    0.15


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    0.79
p-value of test                       :    0.49

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     286
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:15.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.20
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.21
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.26
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:58.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.31
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.36
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.65
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.11
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.11
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  210.21
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  437.51
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:53.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1373.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:00.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.44
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.13
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.24
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:08.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.55
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5026.83
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:58.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45619
p-value of test                       :    0.89


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869619
  j =  1                              :        399908764
  j =  2                              :            45615
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45565
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869565
  j =  1                              :        399908871
  j =  2                              :            45563
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.73e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 8.72e-5
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.31e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.24e-4
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.15
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.64
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:58.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.56
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.86
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   12.12
p-value of test                       :    0.9975

-----------------------------------------------
CPU time used                    :  00:01:47.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.46
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.47e-4
p-value of test                       :    0.9996    *****

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.01
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.42
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:29.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.83
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:28.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  130.75
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:39.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17523.98
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.21
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.58
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.53
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.18
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.52
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:38.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.59
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.02
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.63
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.72
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.09
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  105.78
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.73
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  115.35
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.67
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.38
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.55
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.27
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:44.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.15
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  406.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4864.56
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.40
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.62
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.18
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5113.44
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.72
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  152.35
p-value of test                       :    0.9949


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.27
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :    2.57
p-value of test                       :  5.0e-3



-----------------------------------------------
CPU time used                    :  00:02:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.83
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :    0.13
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:02:25.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.15
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.39e-3
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:46.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:45.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.43
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.45
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.86
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9825.57
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.50
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:03.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:04:14.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.73
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:53.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4985.65
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:53.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.97
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4003.01
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.61
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11882.81
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:29.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.40
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999995633

Normal statistic for number of bits   :  -0.035
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.05
p-value of test                       :    0.55


-----------------------------------------------
Total number of bits:  8000037231

Normal statistic for number of bits   :    0.29
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.44
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.62e-3
p-value of test                       :    0.9984

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.76
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    2.40
p-value of test                       :  8.1e-3

Sample variance                       :    1.62
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:02.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.58

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:14.79

 All tests were passed




Server wird beendet - Lösche Semaphor 46104587.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:41.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:51.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1268
p-value of test                       :    0.9956

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334388
  j =  1                              :        599997464
  j =  2                              :             1268
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1432
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334552
  j =  1                              :        599997136
  j =  2                              :             1432
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5674
p-value of test                       :  3.3e-4    *****


-----------------------------------------------
CPU time used                    :  00:03:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4299
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7198
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:03:09.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:00.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7222
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.37
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.51
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.47
p-value of test                       :    0.78

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     904
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    3.27
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:48.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.60


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    2.22
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     546
p-value of test                       :    0.99

Stat. AD (mNP2)                       :    1.38
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    1.17
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.90
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.65
p-value of test                       :    0.60

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.33
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    1.67
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     129
p-value of test                       :    0.96

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    1.60
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.17
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.44
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.23
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.12
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.26
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.74
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.67
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  268.11
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  400.70
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:53.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.98
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7107.88
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.24
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 9.57e-4
p-value of test                       :    0.9990    *****

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   42.63
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.80
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.64
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:44.40

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5050.50
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:29.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:19.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908300
  j =  2                              :            45844
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:12.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46079
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870079
  j =  1                              :        399907843
  j =  2                              :            46077
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:28.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:02:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:43.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.76e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:24.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.04
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:23.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   85.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.41
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.96
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:57.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.25
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:03.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.24
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:03.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.23
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:19.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:09.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  168.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17551.55
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:00:54.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.23
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.06
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.28
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.33
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.76
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   22.99
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.15
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.15
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.75
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:37.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.69
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.92
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  516.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.64
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.95
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:44.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.07
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.68
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.39
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.64
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.56
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.30
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.35
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  389.53
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  218.58
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  322.58
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.29
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4944.79
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.99
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.64
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.72
p-value of test                       :    0.64


-----------------------------------------------
Normal statistic for number of jumps  :  -0.082
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.68
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :   -0.18
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   -0.34
p-value of test                       :    0.63

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.54
p-value of test                       :    0.94

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.66e-3
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 4.04e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.62e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.28
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.70
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.0e-3

Anderson-Darling statistic = A2       :    2.08
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10224.44
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.04
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.58
p-value of test                       :    0.9950

-----------------------------------------------
CPU time used                    :  00:01:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5021.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.32
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4171.53
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11895.58
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11884.54
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.47
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  7999993239

Normal statistic for number of bits   :  -0.053
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:04.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.55
p-value of test                       :    0.22


-----------------------------------------------
Total number of bits:  7999972344

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:05.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.88
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.78
p-value of test                       :    0.04

Sample variance                       :    0.99
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.48
p-value of test                       :    0.32

Sample variance                       :    1.13
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:39.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 13  BirthdaySpacings, t = 2         3.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 47087627.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:42.03

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:53.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:06.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5455
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4443
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:38.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7357
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:57.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:10.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    1.30
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     898
p-value of test                       :    0.52

Stat. AD (mNP2)                       :    3.07
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.97
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     630
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    1.10
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:17.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.78
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:13.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    2.29
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.57
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.67
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.18
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  260.85
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:53.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1404.05
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6936.65
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.12
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   57.05
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:03:08.76

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :   14.38
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.94
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:36.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4977.20
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:13.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:05.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45882
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869882
  j =  1                              :        399908238
  j =  2                              :            45878
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.55

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46324
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870324
  j =  1                              :        399907356
  j =  2                              :            46316
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:29.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.79e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 5.26e-5
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.18e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.47e-4
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.79
p-value of test                       :  2.6e-3

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.079
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:48.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.79
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.54
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.88
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.99
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.82
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.93
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.45
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.31
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.77
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.83
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.59
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:27.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.19
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:17.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  102.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17478.32
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:00:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   26.10
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.73
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.36
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.19
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.85
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.80
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.77
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.25
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.39
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.28
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.56
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.39
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.04
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.10
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.65
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.92
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  118.76
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.77
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.55
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.22
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.37
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.41
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.08
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4886.50
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  213.17
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.43
p-value of test                       :    0.75


-----------------------------------------------
Normal statistic for number of jumps  :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.88
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -1.22
p-value of test                       :    0.89



-----------------------------------------------
CPU time used                    :  00:02:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    0.72
p-value of test                       :    0.24

Sample variance                       :    2.58
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.47e-3
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 7.28e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:46.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.79
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.30
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.17
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  224.78
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  158.82
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9928.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10010.94
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.46
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:06.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:29.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4929.28
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:53.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4830.70
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3977.02
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4086.48
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:26.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12083.25
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:31.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11594.89
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:30.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.16
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999920036

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.00
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  8000065395

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.70
p-value of test                       :    0.96

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.69
p-value of test                       :    0.24

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.59

Sample variance                       :    0.34
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:46.65

 All tests were passed




Server wird beendet - Lösche Semaphor 48070667.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:43.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:53.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:49.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5367
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7298
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:40.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:57.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4427
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:09.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7342
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7188
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.50
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     840
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.07
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    1.90
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     619
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.73

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.49
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     295
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.65
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:40.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.71
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.90
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.46
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   33.77
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.74
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.39
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  213.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  361.59
p-value of test                       :    0.9952

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1563.53
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:02:01.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7028.27
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.64
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:03:08.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.37
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:44.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.95
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:36.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4971.06
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:03:12.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45538
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869538
  j =  1                              :        399908927
  j =  2                              :            45532
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.03

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45913
p-value of test                       :    0.44


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869913
  j =  1                              :        399908178
  j =  2                              :            45905
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:18.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    2.29
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:55.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:17.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.81e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 8.01e-5
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 2.01e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.059
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.24
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.41
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.98
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.43
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.60
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.83
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.87
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:29.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.76
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:29.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.56
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:39.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17322.81
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.97
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.06
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.92
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.01
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.78
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:37.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.54
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.62
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.20
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.20
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.83
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.72
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.97
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.62
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.96
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.72
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  457.27
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  156.25
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.06
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:45.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.78
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.72
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4989.81
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.71
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  234.80
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.39
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.27
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.13
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.33
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.89
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.36
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    3.34
p-value of test                       :    0.9926


-----------------------------------------------
Normal statistic for number of jumps  :   -0.60
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:02:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.44
p-value of test                       :    0.07

Sample variance                       :    0.97
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.20e-3
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 7.54e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.20e-3
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 9.88e-3
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.87
p-value of test                       :    0.27

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.53
p-value of test                       :    0.07

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:08.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.63
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9901.41
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.82
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:03.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:08.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:04:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5013.69
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:55.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4918.80
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:55.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.05
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.62
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11843.05
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11671.27
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   90.62
p-value of test                       :  1.3e-3


-----------------------------------------------
Total number of bits:  7999901925

Normal statistic for number of bits   :   -0.78
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.44
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000053449

Normal statistic for number of bits   :    0.42
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   0.023
p-value of test                       :    0.49

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    2.33
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:11.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.28
p-value of test                       :    0.61

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.06
p-value of test                       :    0.86

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:11.13

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:59.63

 All tests were passed




Server wird beendet - Lösche Semaphor 49119243.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:40.92

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:51.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:25.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1276
p-value of test                       :    0.9917

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334396
  j =  1                              :        599997448
  j =  2                              :             1276
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5465
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:03:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4523
p-value of test                       :  2.5e-3


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:42.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4347
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4447
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7522
p-value of test                       :  9.0e-3


-----------------------------------------------
CPU time used                    :  00:03:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:08.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7492
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     883
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.24
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.63
p-value of test                       :    0.04

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     604
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.78
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    1.18
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    1.64
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    2.79
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.15
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.10
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:58.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.60
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.01
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:09.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:21.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.48
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.04
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  472.05
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.28
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6971.28
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   25.40
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:03:08.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.23
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  137.92
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:36.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.27
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:13.00

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46128
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870128
  j =  1                              :        399907746
  j =  2                              :            46124
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.15

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45856
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869856
  j =  1                              :        399908290
  j =  2                              :            45852
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.22


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:18.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:47.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:02.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.60e-4
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 4.83e-5
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.07
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.75
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.11
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:42.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.59
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.97
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.98
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.53
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:50.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.42
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.45
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.25
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:46.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:03.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.37
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:03.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.13
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.37
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.61
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:09.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17432.85
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.53
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   18.33
p-value of test                       :    0.9909


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.38
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.23
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.31
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.54
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.36
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.54
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.10
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:38.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.96
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.45
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  486.12
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.21
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  108.49
p-value of test                       :    0.9913


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.91
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  478.88
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  433.40
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5045.55
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.11
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.82
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:36.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.13
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  331.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.40
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.13
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.58
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.08
p-value of test                       :    0.09


-----------------------------------------------
Normal statistic for number of jumps  :    1.47
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:25.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.00e-3
p-value of test                       :    0.9925

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.60e-3
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:46.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 8.12e-3
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.53
p-value of test                       :    0.96

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:28.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:25.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  215.16
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  180.79
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9887.30
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:00.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.53
p-value of test                       :  1.8e-3

Anderson-Darling statistic = A2       :    3.69
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10337.79
p-value of test                       :  9.0e-3

-----------------------------------------------
CPU time used                    :  00:01:01.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.79
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4919.56
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4944.66
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4242.77
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4184.53
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11733.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12061.05
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:31.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.35
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999792260

Normal statistic for number of bits   :   -1.64
p-value of test                       :    0.95



-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   85.49
p-value of test                       :  4.1e-3


-----------------------------------------------
Total number of bits:  7999917150

Normal statistic for number of bits   :   -0.65
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Tests on the sum of all N observations
Standardized normal statistic         :    0.40
p-value of test                       :    0.35

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :   -0.94
p-value of test                       :    0.83

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:26.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.68

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:12.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:48.77

 All tests were passed




Server wird beendet - Lösche Semaphor 49971211.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:40.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1457
p-value of test                       :  6.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334577
  j =  1                              :        599997086
  j =  2                              :             1457
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5432
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4219
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:42.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7435
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7503
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:12.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:09.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:14.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.31
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.87
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.66
p-value of test                       :    0.59


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.13
p-value of test                       :    0.30

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.12
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    1.94
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    0.26
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.99
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.11
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:56.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.33
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:00.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.39
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.13
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.09
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  179.83
p-value of test                       :    0.9953

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  412.77
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1465.07
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6994.36
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.01
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:13.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.65
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:46.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.09
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:42.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4760.76
p-value of test                       :    0.9976


-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:55.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46126
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870126
  j =  1                              :        399907751
  j =  2                              :            46120
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.40

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46078
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870078
  j =  1                              :        399907850
  j =  2                              :            46066
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.54


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:19.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.12e-4
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.57e-5
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.16
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:42.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.66
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:50.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.76
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   69.03
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:00:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   21.83
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.52
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.13
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:28.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:28.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.65
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.13
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.30
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.17
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   21.92
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.16
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.04
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.73
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.28
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.41
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.45
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.18
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:37.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.31
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.64
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.66
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.08
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:45.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.09
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  143.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.12
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.68
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   67.55
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:45.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.05
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.48
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5007.88
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.32
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  223.40
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:37.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.49
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.82
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4933.60
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.88
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  173.90
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:37.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.29
p-value of test                       :    0.08


-----------------------------------------------
Normal statistic for number of jumps  :   -1.51
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:02:25.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.25
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:26.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9941

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 5.60e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.97
p-value of test                       :    0.15

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.66
p-value of test                       :    0.57

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:30.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.70
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:13.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:09.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10119.28
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.92
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.66
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.019
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:04:40.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4797.20
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:53.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.65
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4121.83
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:22.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4080.50
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12027.07
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11845.97
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.51
p-value of test                       :    0.18


-----------------------------------------------
Total number of bits:  8000055951

Normal statistic for number of bits   :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:01:08.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   53.33
p-value of test                       :    0.50


-----------------------------------------------
Total number of bits:  7999883520

Normal statistic for number of bits   :   -0.92
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:01:10.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Tests on the sum of all N observations
Standardized normal statistic         :   -0.39
p-value of test                       :    0.65

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:17.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.23
p-value of test                       :    0.89

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:24.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.50
p-value of test                       :    0.31

Sample variance                       :    1.45
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:17.69

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:52.64

 All tests were passed




Server wird beendet - Lösche Semaphor 50921483.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:39.86

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:50.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1398
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334518
  j =  1                              :        599997204
  j =  2                              :             1398
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.66

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:48.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:03:56.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7415
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:42.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:01.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:03:13.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:13.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7396
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:04:16.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     916
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.93
p-value of test                       :    0.03

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     603
p-value of test                       :    0.46

Stat. AD (mNP2)                       :    1.59
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.09
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    1.81
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     323
p-value of test                       :    0.10

Stat. AD (mNP2)                       :    1.29
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.25
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     167
p-value of test                       :    0.09

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.05
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.87
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.80
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.64
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.67
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.76
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  387.91
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1224.26
p-value of test                       : 1 -  1.5e-5    *****

-----------------------------------------------
CPU time used                    :  00:02:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7256.42
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:57.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.40
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:03:11.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    0.20
p-value of test                       :    0.9991    *****


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  117.24
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:01:41.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4956.98
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:18.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46029
p-value of test                       :    0.24


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870029
  j =  1                              :        399907948
  j =  2                              :            46017
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46045
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870045
  j =  1                              :        399907915
  j =  2                              :            46035
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:19.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.88e-4
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.09e-5
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.55
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.33
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:51.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.78
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   91.53
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.75
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   57.88
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:57.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.26
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.79e-3
p-value of test                       :    0.9916

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.44
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.29
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.26
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.51
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.58
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:29.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:19.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.059
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:10.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  128.48
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.01
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:00:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.66
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.28
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.26
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.44
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.67
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.66
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.18
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.01
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.02
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  181.39
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.98
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.39
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.84
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.48
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.58
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.31
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  174.14
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.55
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:43.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.18
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  414.96
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4949.11
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.52
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.11
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.51
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.92
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.38
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  354.43
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:35.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    1.21
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.48
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.81
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    1.20
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.82e-3
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:46.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.96
p-value of test                       :    0.94

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.17
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.40
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.49
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:07.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10056.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10242.98
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -2.23
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:05:14.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4862.02
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:51.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4885.74
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:57.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4055.07
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.61
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11869.19
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11796.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.94
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  8000050152

Normal statistic for number of bits   :    0.40
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.17
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999967784

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:25.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.41e-3
p-value of test                       :    0.9975

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    2.03
p-value of test                       :    0.02

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:18.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.66
p-value of test                       :    0.95

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.05e-3
p-value of test                       :    0.9936

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.82
p-value of test                       :    0.03

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.43

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:08.72
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 36  Gap, r = 0                     1 -  1.5e-5
 40  Permutation, t = 3              0.9991 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52199435.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:42.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1317
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334437
  j =  1                              :        599997366
  j =  2                              :             1317
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1273
p-value of test                       :    0.9934

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334393
  j =  1                              :        599997454
  j =  2                              :             1273
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:55.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:42.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:43.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4179
p-value of test                       :    0.9918


-----------------------------------------------
CPU time used                    :  00:02:01.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:12.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7251
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:12.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:15.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.20
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.63
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.03
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.59
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.55
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     297
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    2.19
p-value of test                       :    0.07

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.50


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.46
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:44.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.15
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.00
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.12
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.24
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:12.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.62
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.72
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.35
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  235.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  453.49
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1390.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7019.70
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:53.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   19.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.07
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:19.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.75
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:46.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.77
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5049.06
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:24.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:07.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45929
p-value of test                       :    0.41


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869929
  j =  1                              :        399908145
  j =  2                              :            45923
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45818
p-value of test                       :    0.61


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869818
  j =  1                              :        399908365
  j =  2                              :            45816
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:33.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:08.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:19.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:37.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.36e-4
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    : 1.20e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.52e-4
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 7.43e-5
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.23
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.51
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.067
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:48.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.87
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:57.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.94
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   21.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.03
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    : 8.01e-3
p-value of test                       :    0.9914

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.61
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   54.70
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.92
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:28.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.19
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:28.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    6.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:08.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  135.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.52
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   21.02
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.48
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.90
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.30
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.42
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.87
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.26
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.67
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.00
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.72
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:37.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.21
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  110.95
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.50
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.82
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:45.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.02
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.32
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  537.27
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.52
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.95
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.21
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.10
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.02
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.05
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.92
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  329.04
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5055.38
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.97
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.10
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.55
p-value of test                       :    0.89


-----------------------------------------------
Normal statistic for number of jumps  :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:26.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.50
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:02:26.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.58e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:46.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.33e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.70
p-value of test                       :    0.37

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.43
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.06
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10054.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10196.18
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:04.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.34
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:09.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:04:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.72
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5018.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:00.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4099.23
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4064.43
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11695.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:35.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11989.20
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.72
p-value of test                       :    0.31


-----------------------------------------------
Total number of bits:  7999979205

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   67.38
p-value of test                       :    0.10


-----------------------------------------------
Total number of bits:  8000091375

Normal statistic for number of bits   :    0.72
p-value of test                       :    0.24



-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.59
p-value of test                       :    0.94

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.37
p-value of test                       :    0.65

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:24.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.46
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:15.61

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:08.98

 All tests were passed




Server wird beendet - Lösche Semaphor 53379083.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:50.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1261
p-value of test                       :    0.9975

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334381
  j =  1                              :        599997478
  j =  2                              :             1261
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1459
p-value of test                       :  5.7e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334579
  j =  1                              :        599997082
  j =  2                              :             1459
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5595
p-value of test                       :  9.5e-3


-----------------------------------------------
CPU time used                    :  00:03:58.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4303
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7319
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:14.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.45
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     925
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.37
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     626
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     311
p-value of test                       :    0.27

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    2.47
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.06
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.73
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     163
p-value of test                       :    0.15

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.85
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.15
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.96
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.55
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.42
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.01
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.34
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:26.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  359.93
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:01:56.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1511.36
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:03.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7040.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   59.31
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:03:20.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.31
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:53.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.13
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:01:40.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4937.46
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:01.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45852
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869852
  j =  1                              :        399908301
  j =  2                              :            45842
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45873
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869873
  j =  1                              :        399908260
  j =  2                              :            45861
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:32.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.07


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:58.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.09e-5
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.11e-4
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 4.17e-5
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.35
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:48.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.68
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.76
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   39.67
p-value of test                       :    0.9968

-----------------------------------------------
CPU time used                    :  00:00:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.45
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.27
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   23.32
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.92
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   46.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:50.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.96
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.31
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:29.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.48
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.27
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:09.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  123.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17153.27
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.63
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.91
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.70
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.29
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.39
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.11
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.51
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.87
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.28
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.00
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.86
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.75
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.88
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.66
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.67
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  124.45
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.83
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.44
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.71
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.33
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:44.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.81
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.65
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5148.39
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.84
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.32
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.26
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  357.09
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5021.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  413.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  150.53
p-value of test                       :    0.9963


-----------------------------------------------
CPU time used                    :  00:00:35.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.55
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :   -0.85
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.88
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.97
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    1.32
p-value of test                       :    0.09

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:46.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.75e-3
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 4.65e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.98
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.44

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.01
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.43
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.77
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9853.56
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10089.81
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.43
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.45
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:06.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4775.85
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:58.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:58.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4061.10
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.22
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11516.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:34.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.38
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.29
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999934019

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:03.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.50
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  8000164512

Normal statistic for number of bits   :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:01:06.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Tests on the sum of all N observations
Standardized normal statistic         :    1.72
p-value of test                       :    0.04

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.27e-4
p-value of test                       :    0.9994    *****

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.73
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.91
p-value of test                       :  1.8e-3

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   0.093
p-value of test                       :    0.46

Sample variance                       :    0.78
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.68
p-value of test                       :    0.75

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:46.84

 All tests were passed




Server wird beendet - Lösche Semaphor 54427659.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:48.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5403
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:03:55.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7147
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:42.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:11.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7434
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:04:09.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.85

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     906
p-value of test                       :    0.43

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.75
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.68
p-value of test                       :    0.58

Stat. AD after spacings (mNP2-S)      :    4.69
p-value of test                       :  4.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.40
p-value of test                       :    0.85

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     310
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    2.60
p-value of test                       :    0.04

Stat. AD after spacings (mNP2-S)      :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.39
p-value of test                       :    0.86

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.42

Stat. AD after spacings (mNP2-S)      :    1.12
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:02:46.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.73
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:08.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.90
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:11.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:10.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.30
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   32.44
p-value of test                       :    0.9912

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:22.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   80.09
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.56
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.60
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  423.67
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:50.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1429.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:02.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7070.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.36
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:03:11.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.76
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:45.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.61
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5103.26
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:05.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45955
p-value of test                       :    0.36


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869955
  j =  1                              :        399908094
  j =  2                              :            45947
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46047
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870047
  j =  1                              :        399907908
  j =  2                              :            46043
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    2.74
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:32.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :  2.1e-3

Anderson-Darling statistic = A2       :    2.67
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.022
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:18.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.82e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 2.12e-4
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.27
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.99
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.62
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.70
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.83
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.77
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.90
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.07
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:50.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.49
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.14
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.36
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   45.52
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.15
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.15
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.85
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:29.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.78
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:17.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17403.23
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   24.98
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.07
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.20
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.61
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.75
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:38.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.34
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.90
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.38
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.27
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.92
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.34
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  446.77
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  123.32
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   90.63
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.46
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  448.00
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.56
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.97
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.55
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  305.30
p-value of test                       :    0.9988


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4908.88
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.66
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.91
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:35.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.97
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.24
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4835.34
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.39
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  208.26
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   20.71
p-value of test                       :    0.05


-----------------------------------------------
Normal statistic for number of jumps  :   -1.70
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:22.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.86
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :   -2.52
p-value of test                       :    0.9941



-----------------------------------------------
CPU time used                    :  00:02:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.29
p-value of test                       :    0.39

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.45
p-value of test                       :    0.33

Sample variance                       :    1.26
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.75e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.28e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 8.82e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.95
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   13.17
p-value of test                       :    0.11

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.59
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  201.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:07.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10085.78
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10140.04
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.57
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:04:10.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.60
p-value of test                       :  2.8e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    5.16
p-value of test                       :  2.5e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4607.65
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:51.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4748.85
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:51.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.57
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:22.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4010.94
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11839.63
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:28.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11928.48
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.60
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000098527

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.47
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  8000081514

Normal statistic for number of bits   :    0.64
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:05.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    0.89
p-value of test                       :    0.19

Sample variance                       :    2.63
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.22
p-value of test                       :    0.41

Sample variance                       :    1.58
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:03.40

 All tests were passed




Server wird beendet - Lösche Semaphor 55509003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:49.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:53.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1422
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334542
  j =  1                              :        599997156
  j =  2                              :             1422
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5451
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:03:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4267
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:41.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7270
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4359
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:00.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:03:11.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:12.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7157
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:04:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7309
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:04:10.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     851
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.04
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.50
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.40
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     570
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    4.08
p-value of test                       :  8.0e-3

-----------------------------------------------
CPU time used                    :  00:01:15.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.10
p-value of test                       :    0.31

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.43

Stat. AD after spacings (mNP2-S)      :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:15.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.62


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.54
p-value of test                       :    0.70

Test on the Nm values of W_{n,i}(mNP1):    1.33
p-value of test                       :    0.22

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.84
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    1.94
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.08
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:57.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.49
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:06.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.82
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:00.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.08
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:10.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.62
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.58
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.16
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.80
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1530.66
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.95
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.60
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.73
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:14.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.80
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:46.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  121.44
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:41.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5095.57
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:20.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:04.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46022
p-value of test                       :    0.25


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870022
  j =  1                              :        399907960
  j =  2                              :            46014
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907810
  j =  2                              :            46089
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.13
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:38.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.63e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 1.31e-4
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 9.05e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.79
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:49.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:49.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.63
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.91
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.39
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.26
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.67
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.77
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.92
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.12
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:28.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.42
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:27.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.56
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:08.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  144.88
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:41.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17442.21
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:00:53.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.16
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.08
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.47
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.24
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.64
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.65
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.78
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.42
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   43.04
p-value of test                       :  9.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   38.09
p-value of test                       :  2.4e-3


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  125.96
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.89
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  515.26
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.05
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.67
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.86
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.89
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  470.85
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.92
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   74.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:43.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.44
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.63
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5024.76
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  341.58
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  187.30
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:35.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  385.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  360.50
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5042.25
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.06
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  210.47
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:35.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.60
p-value of test                       :    0.65


-----------------------------------------------
Normal statistic for number of jumps  :  -0.069
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.36
p-value of test                       :    0.50


-----------------------------------------------
Normal statistic for number of jumps  :   -1.05
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:22.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:05.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.41e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 9.13e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 8.79e-3
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.52
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.24
p-value of test                       :    0.51

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.48
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:06.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.17
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10074.67
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:00.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9930.69
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:04:16.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4851.83
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4715.93
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:55.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4308.70
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.88
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11934.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12008.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:32.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.73
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000030745

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.23
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999922769

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    0.82
p-value of test                       :    0.20

Sample variance                       :    0.22
p-value of test                       :    0.9916

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.3e-3

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.49
p-value of test                       :  6.4e-3

Sample variance                       :    0.51
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:11.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.74
p-value of test                       :    0.04

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:23.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.73
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:19.57

 All tests were passed




Server wird beendet - Lösche Semaphor 56492043.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:49.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5448
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4235
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7514
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:44.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4261
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:01.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4382
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7420
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:13.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7296
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:08.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7368
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:04:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.46
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.31
p-value of test                       :    0.23

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:50.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.62
p-value of test                       :    0.63


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.23
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    1.05
p-value of test                       :    0.33

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     615
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:15.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.14
p-value of test                       :    0.29


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     306
p-value of test                       :    0.37

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    1.65
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:17.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.42
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.77
p-value of test                       :    0.12

Stat. AD after spacings (mNP2-S)      :    1.84
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:46.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.51
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:06.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.49
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.47
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.50
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.30
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:25.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  254.50
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  399.25
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:54.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1468.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7069.06
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.83
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   75.36
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:15.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  104.20
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4974.78
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:02:57.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45774
p-value of test                       :    0.69


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869774
  j =  1                              :        399908455
  j =  2                              :            45768
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45784
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869784
  j =  1                              :        399908436
  j =  2                              :            45776
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:32.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.87


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:21.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.67


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:19.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.62e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.91e-4
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.61e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 1.43e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.09
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.48
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.095
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.71
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.06
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.66
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.16
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:58.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   61.14
p-value of test                       :  7.5e-3

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   45.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:47.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.46
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:04.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.54
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:28.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:16.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.16
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  150.45
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:41.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17663.03
p-value of test                       :    0.11



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.68
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.26
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.01
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.76
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.79
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.71
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   24.99
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.79
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.19
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.44
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.61
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.73
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.10
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.70
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.76
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  136.25
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.35
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.72
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.70
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.09
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.31
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.04
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4838.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.09
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  244.78
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:36.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.54
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.41
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5047.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.85
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:35.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.25
p-value of test                       :    0.95


-----------------------------------------------
Normal statistic for number of jumps  :    0.95
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:25.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.15
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:24.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :   0.071
p-value of test                       :    0.47

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:03.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    1.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:46.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 4.81e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.14
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.00
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:06.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.35
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9957.41
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10020.04
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.58
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.28
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:04:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4880.65
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4769.31
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4102.98
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:24.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.72
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11848.53
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:32.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.19
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:33.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.31
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000225625

Normal statistic for number of bits   :    1.78
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.03
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  8000002941

Normal statistic for number of bits   :   0.023
p-value of test                       :    0.49



-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :   -1.20
p-value of test                       :    0.88

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :    1.25
p-value of test                       :    0.10

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:13.37

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:19.26

 All tests were passed




Server wird beendet - Lösche Semaphor 57540619.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:38.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:31.62

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1400
p-value of test                       :    0.17

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334520
  j =  1                              :        599997200
  j =  2                              :             1400
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:59.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:43.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:59.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7324
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:03:10.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:10.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7360
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:08.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.11
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     891
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.67
p-value of test                       :    0.58

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.93
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.98
p-value of test                       :    0.37

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.73
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     152
p-value of test                       :    0.45

Stat. AD (mNP2)                       :    0.22
p-value of test                       :    0.99

Stat. AD after spacings (mNP2-S)      :    1.55
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.90
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:04.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.06
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:12.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.24
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.95
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.41
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:21.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.97
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  455.51
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:02.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7051.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:50.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:16.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   58.37
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:03:08.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.70
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  135.26
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:36.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5089.94
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:13.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:03:03.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45676
p-value of test                       :    0.83


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869676
  j =  1                              :        399908651
  j =  2                              :            45670
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45722
p-value of test                       :    0.77


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869722
  j =  1                              :        399908562
  j =  2                              :            45710
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    : 7.91e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:29.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.33
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :  1.0e-2


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:05.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:18.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:36.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.18e-5
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    : 2.02e-4
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.14e-4
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    : 7.15e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.77
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.27
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:44.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.045
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:46.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.96
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.23
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.28
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.37
p-value of test                       :  5.7e-3

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.93
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.23
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.81
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:04.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.12
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.23
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.27
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.73
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:39.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17336.91
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.77
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.06
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.88
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.85
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:37.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.99
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.33
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.22
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.35
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.75
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.95
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.11
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.17
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.15
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.94
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  199.55
p-value of test                       :  2.2e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.08
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.03
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.27
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.64
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.08
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.48
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  375.02
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.28
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.90
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  413.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5046.67
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.86
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.78
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:35.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.27
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    1.57
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:02:25.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.18
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -1.00
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.84e-3
p-value of test                       :    0.9949

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Tests on the sum of all N observations
Standardized normal statistic         :   -1.29
p-value of test                       :    0.90

Sample variance                       :    1.21
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.33
p-value of test                       :    0.91

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.99e-3
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:45.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.91e-3
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.23
p-value of test                       :    0.62

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.04
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.09
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.30
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10120.02
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9767.56
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.32
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.65
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:12.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4893.68
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:52.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4677.55
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:52.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3973.32
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4251.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11874.41
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11835.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.31
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000031711

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:03.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   33.25
p-value of test                       :    0.99


-----------------------------------------------
Total number of bits:  8000017593

Normal statistic for number of bits   :    0.14
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :    0.19
p-value of test                       :    0.43

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.58
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :    0.52
p-value of test                       :    0.30

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:06.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.76

 All tests were passed




Server wird beendet - Lösche Semaphor 58589195.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:40.11

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:49.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1396
p-value of test                       :    0.20

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334516
  j =  1                              :        599997208
  j =  2                              :             1396
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:08.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5286
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:03:56.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4336
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:42.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7183
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:42.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4371
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:01:59.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7274
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7235
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.62
p-value of test                       :    0.04


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.72
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     884
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    3.13
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    1.32
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     623
p-value of test                       :    0.18

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.52
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9973

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.58
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    1.58
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     145
p-value of test                       :    0.64

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.20
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:56.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   19.18
p-value of test                       :  7.6e-3

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.82
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.01
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:07.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:11.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   71.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:22.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.12
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  459.94
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1490.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7188.97
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.05
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:03:09.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.03
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.65

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   98.92
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:37.03

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5034.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:12.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:04.18

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45764
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869764
  j =  1                              :        399908478
  j =  2                              :            45752
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45411
p-value of test                       :    0.99


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869411
  j =  1                              :        399909181
  j =  2                              :            45405
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.53
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:29.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:19.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:46.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:02:07.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.10e-4
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    : 1.39e-5
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.32e-4
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.12
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.13
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.19
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.94
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:58.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.07
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:57.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.30
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.68
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.85
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:27.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.81
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:39.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17485.85
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:00:53.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.95
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.63
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.80
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:37.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.75
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.01
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.14
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   12.20
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.14
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.94
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.00
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  482.58
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.49
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.98
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:45.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.35
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.75
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.75
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.77
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.79
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.92
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  348.42
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5034.93
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  370.70
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.64
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.76
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.81
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.40
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  360.41
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.65
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.58
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :    1.41
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:02:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.71
p-value of test                       :    0.97


-----------------------------------------------
Normal statistic for number of jumps  :    0.39
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :   -0.50
p-value of test                       :    0.69

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:06.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.66e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.61
p-value of test                       :    0.13

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.15
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.38
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9896.58
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9998.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.21
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:04:11.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4988.00
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.92
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.67
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4216.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11937.59
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:29.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.17
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.39
p-value of test                       :    0.58


-----------------------------------------------
Total number of bits:  7999936647

Normal statistic for number of bits   :   -0.50
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.49
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999929399

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :  -0.084
p-value of test                       :    0.53

Sample variance                       :    0.76
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.35
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.23
p-value of test                       :    0.11

Sample variance                       :    1.88
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:24.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.41
p-value of test                       :    0.66

Sample variance                       :    0.45
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:05.73

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:12.84

 All tests were passed




Server wird beendet - Lösche Semaphor 59605003.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:39.10

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1304
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334424
  j =  1                              :        599997392
  j =  2                              :             1304
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1359
p-value of test                       :    0.55

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334479
  j =  1                              :        599997282
  j =  2                              :             1359
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5420
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:56.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4258
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:41.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:02:41.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4325
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7329
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:09.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7271
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:04:03.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:07.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.61
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.99
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     913
p-value of test                       :    0.34

Stat. AD (mNP2)                       :    0.79
p-value of test                       :    0.49

Stat. AD after spacings (mNP2-S)      :    2.11
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.46
p-value of test                       :    0.19

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:14.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.34
p-value of test                       :    0.91


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.30
p-value of test                       :    0.23

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     289
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.10
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.90
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:02:44.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:55.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.73
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.65
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.97
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:09.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.32
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.22
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.09
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:22.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.85
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  374.50
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1576.97
p-value of test                       :  5.5e-3

-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7017.38
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:51.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:16.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   51.83
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:03:08.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.03
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:45.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  125.52
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:36.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4980.95
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:04.96

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46137
p-value of test                       :    0.12


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870137
  j =  1                              :        399907731
  j =  2                              :            46127
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:50.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45768
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869768
  j =  1                              :        399908465
  j =  2                              :            45766
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:29.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:04.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    2.60
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:18.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:37.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-4
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 3.97e-5
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.38e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 5.47e-5
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:24.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      : 6.08e-3
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:47.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.86
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.43
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.76
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.67
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.07
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:49.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.89
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.98
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:48.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.75
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.49
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.70
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   12.18
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:19.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.91
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  107.16
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:39.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17439.64
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:00:53.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.13
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.81
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.91
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.23
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.33
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.29
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.95
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.06
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.88
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.28
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:38.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.33
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.10
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  488.89
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.43
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.41
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.90
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.01
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  509.52
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  125.95
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.26
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  375.08
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  405.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4968.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.26
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:35.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.87
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5061.61
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.31
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  192.74
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:35.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.11
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :   -1.28
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:02:24.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.09
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :   -0.62
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   0.011
p-value of test                       :    0.50

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :    1.45
p-value of test                       :    0.07

Sample variance                       :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.55e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    : 4.89e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:43.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.27
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.21
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.1e-3

Kolmogorov-Smirnov- statistic = D-    : 4.98e-3
p-value of test                       :    0.9948

Anderson-Darling statistic = A2       :    4.73
p-value of test                       :  4.1e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  150.94
p-value of test                       :    0.9960

-----------------------------------------------
CPU time used                    :  00:02:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.94e-3
p-value of test                       :    0.9970

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    5.49
p-value of test                       :  1.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  273.11
p-value of test                       :  4.5e-4    *****

-----------------------------------------------
CPU time used                    :  00:02:05.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9952.24
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10066.41
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:06.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.19
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:05.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.76
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:04:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4771.79
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4993.25
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4150.26
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4108.22
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11838.04
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11714.43
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:30.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.02
p-value of test                       :    0.21


-----------------------------------------------
Total number of bits:  7999862769

Normal statistic for number of bits   :   -1.08
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:01:04.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.44
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  8000099037

Normal statistic for number of bits   :    0.78
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :  -0.071
p-value of test                       :    0.53

Sample variance                       :    0.54
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.54
p-value of test                       :    0.70

Sample variance                       :    0.23
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   0.036
p-value of test                       :    0.49

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.19

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:20.63
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 89  PeriodsInStrings, r = 20        4.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 60653579.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:41.45

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5453
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:03:55.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4348
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:41.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7358
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:40.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4298
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4207
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7295
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7332
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:11.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:04:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    0.73
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     861
p-value of test                       :    0.90

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9921

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:50.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.11


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.53
p-value of test                       :    0.72

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     642
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.19
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.55
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    1.20
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     281
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:16.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    1.69
p-value of test                       :    0.14

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.61
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:08.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.14
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.70
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.09
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  239.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  445.67
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1447.29
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7086.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   21.95
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:13.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   68.82
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:03:08.55

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.32
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:44.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   73.09
p-value of test                       :    0.9997    *****


-----------------------------------------------
CPU time used                    :  00:01:36.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5001.58
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:12.98

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:04.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45965
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869965
  j =  1                              :        399908073
  j =  2                              :            45959
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.26

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46016
p-value of test                       :    0.26


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870016
  j =  1                              :        399907971
  j =  2                              :            46010
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 2.83e-3
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.08


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:17.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.50e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.48e-4
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:22.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 2.44e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.093
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.56
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:41.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.07
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.04
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:55.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.64
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.90
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:57.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.51
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   36.98
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.020
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.12
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.01
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.25
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:29.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.77
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:19.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.51
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.15
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:40.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17630.10
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:00:54.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.94
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.56
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.87
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   38.83
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.78
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.71
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.08
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.46
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.13
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.81
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.12
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.88
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  517.34
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  141.04
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.30
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  133.77
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  206.03
p-value of test                       :  1.0e-4    *****


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.63
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.40
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.74
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4898.63
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  395.13
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.42
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  387.61
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.92
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5128.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  380.35
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  232.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.55
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.07
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :    1.99
p-value of test                       :    0.02



-----------------------------------------------
CPU time used                    :  00:02:26.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.16
p-value of test                       :    0.88

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    2.09
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:06.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.88e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.58e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:45.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.47
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.08
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.80
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9811.65
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10065.51
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.05
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.25
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:17.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.14
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:53.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4897.40
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:53.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4169.45
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.09
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11910.64
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12019.20
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:30.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.27
p-value of test                       :    0.90


-----------------------------------------------
Total number of bits:  8000013090

Normal statistic for number of bits   :    0.10
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.48
p-value of test                       :    0.61


-----------------------------------------------
Total number of bits:  7999952016

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Tests on the sum of all N observations
Standardized normal statistic         :    1.15
p-value of test                       :    0.13

Sample variance                       :    0.60
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    1.50
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Tests on the sum of all N observations
Standardized normal statistic         :    1.51
p-value of test                       :    0.07

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:08.26

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:31.07
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 41  Permutation, t = 5              0.9997 
 77  RandomWalk1 R (L=1000, r=20)    1.0e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61669387.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:40.61

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:04.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5459
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4366
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:41.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7164
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4350
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:58.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4455
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:03:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7267
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:04:05.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.01
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    1.45
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     869
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.75
p-value of test                       :    0.52

Stat. AD after spacings (mNP2-S)      :    1.75
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.89
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.92

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     628
p-value of test                       :    0.13

Stat. AD (mNP2)                       :    0.32
p-value of test                       :    0.92

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.16
p-value of test                       :    0.9974


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.31
p-value of test                       :    0.93

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.87
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:15.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     172
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    1.34
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    1.67
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:42.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.47
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.86
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:09.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.98
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:10.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.58
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.90
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  211.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  390.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1386.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:02:00.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.90
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   53.43
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.40
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:45.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  140.61
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5046.21
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45683
p-value of test                       :    0.82


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869683
  j =  1                              :        399908635
  j =  2                              :            45681
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.72

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46243
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870243
  j =  1                              :        399907518
  j =  2                              :            46235
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 7.36e-4
p-value of test                       :    0.9992    *****

Anderson-Darling statistic = A2       :    4.18
p-value of test                       :  7.2e-3


-----------------------------------------------
CPU time used                    :  00:02:30.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.49


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:18.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:49.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:05.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:56.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:18.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:36.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.28e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.80e-4
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 2.47e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.65
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.91
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:23.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:46.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:50.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:57.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.99
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   54.19
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.49
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.97
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.99
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   61.41
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:03.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:03.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:26.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:16.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.23
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17279.43
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.77
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.78
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.15
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.30
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   54.56
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.07
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.87
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   34.21
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.99
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.36
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.19
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.50
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.26
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.55
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:42.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.27
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.59
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  452.63
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  171.69
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.58
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.49
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  334.36
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5183.92
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  393.75
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.83
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:34.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  439.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.60
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.53
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.60
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  212.81
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:33.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.68
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :    1.71
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:02:19.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.07
p-value of test                       :    0.15


-----------------------------------------------
Normal statistic for number of jumps  :   -0.45
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.60

Sample variance                       :    0.69
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.60
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.6e-3

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:07.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.74e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 9.19e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.06
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.76
p-value of test                       :    0.28

-----------------------------------------------
Global longest run of 1               :   29.00
p-value of test                       :    0.9905



-----------------------------------------------
CPU time used                    :  00:01:17.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  238.79
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  174.00
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10008.58
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9808.55
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:58.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.34
p-value of test                       :    0.9903

-----------------------------------------------
CPU time used                    :  00:00:54.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.62
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.74
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:20.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4903.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4837.13
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:47.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4156.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:18.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4070.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11931.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11883.35
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.41
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  7999927833

Normal statistic for number of bits   :   -0.57
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.10
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  7999871619

Normal statistic for number of bits   :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:58.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.24
p-value of test                       :    0.11

Sample variance                       :    0.48
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.53
p-value of test                       :    0.94

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :  -0.095
p-value of test                       :    0.54

Sample variance                       :    0.87
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:16.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:58.46

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:03:11.72

 All tests were passed




Server wird beendet - Lösche Semaphor 62717963.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:47.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:01.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:42.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:43.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:21.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1415
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334535
  j =  1                              :        599997170
  j =  2                              :             1415
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1469
p-value of test                       :  2.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334589
  j =  1                              :        599997062
  j =  2                              :             1469
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1300
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334420
  j =  1                              :        599997400
  j =  2                              :             1300
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:39.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:43.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:36.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:35.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:54.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7238
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7290
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:01.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.79
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    1.61
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     865
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.59
p-value of test                       :    0.66

Stat. AD after spacings (mNP2-S)      :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:51.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.12
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.85
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    1.15
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.26
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.40
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.27
p-value of test                       :    0.96

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:33.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.36
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.21
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:07.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.03
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.85
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:11.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.48
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:10.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.31
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.81
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.86
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  199.09
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:24.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  427.00
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1430.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:05.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7145.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:50.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   61.85
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.62
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  155.01
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:39.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5032.26
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45992
p-value of test                       :    0.30


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869992
  j =  1                              :        399908020
  j =  2                              :            45984
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45748
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869748
  j =  1                              :        399908509
  j =  2                              :            45738
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:02:32.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:02:19.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.78e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.40e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.24e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.48e-4
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:22.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.17
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.35
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.28
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.33
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:57.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:51.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.75
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:57.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.45
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   16.42
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.91
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.62
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:08.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.54
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:07.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.22
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    8.55
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:29.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.79
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  132.28
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:41.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17483.89
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:58.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.74
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.59
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.90
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.76
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.27
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.74
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.33
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.83
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.64
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:42.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.87
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.28
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  502.74
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.32
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.77
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.77
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.89
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  500.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  131.62
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  100.54
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:47.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.05
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.89
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5114.50
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  427.70
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.77
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  352.11
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.32
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.90
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.33
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.22
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:33.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.89
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:02:13.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.07
p-value of test                       :    0.24


-----------------------------------------------
Normal statistic for number of jumps  :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:02:13.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:11.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.52
p-value of test                       :    0.70

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 5.90e-3
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:48.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 5.55e-3
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.95
p-value of test                       :    0.35

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:26.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.09
p-value of test                       :    0.53

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.69
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:02:11.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.37
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:10.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10046.54
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:00.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9920.97
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:10.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.47
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4876.76
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4954.57
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4286.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:22.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4142.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11777.57
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11816.45
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:32.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.33
p-value of test                       :    0.98


-----------------------------------------------
Total number of bits:  7999979469

Normal statistic for number of bits   :   -0.16
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:06.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   27.04
p-value of test                       :    0.9992    *****


-----------------------------------------------
Total number of bits:  7999945998

Normal statistic for number of bits   :   -0.43
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:27.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.26
p-value of test                       :    0.60

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.42
p-value of test                       :    0.66

Sample variance                       :    1.18
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:29.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:57.81
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 102  Run of bits, r = 27             0.9992 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 42336268.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.9934


-----------------------------------------------
CPU time used                    :  00:00:47.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:55.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:47.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1387
p-value of test                       :    0.27

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334507
  j =  1                              :        599997226
  j =  2                              :             1387
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:22.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:24.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:17.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5492
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:03:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:39.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7292
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:38.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4329
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:01:58.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:09.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7409
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    1.25
p-value of test                       :    0.25

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     864
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    1.71
p-value of test                       :    0.13

Stat. AD after spacings (mNP2-S)      :    2.89
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:46.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.47
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.69
p-value of test                       :    0.57

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     624
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:11.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.87
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     298
p-value of test                       :    0.53

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:02:12.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    2.30
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:44.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.46
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.11
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.56
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.00
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:07.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   30.11
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.53
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.67
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:32.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.57
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1411.70
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6912.89
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.20
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:18.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.00
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.69
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:50.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.97
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5153.11
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:01:34.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:17.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45753
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869753
  j =  1                              :        399908498
  j =  2                              :            45745
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46333
p-value of test                       :    0.02


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870333
  j =  1                              :        399907341
  j =  2                              :            46319
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.54
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:31.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.85


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:53.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 6.22e-3
p-value of test                       :    0.9930

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:19.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:37.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.84e-5
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.38
p-value of test                       :  8.7e-3

-----------------------------------------------
CPU time used                    :  00:01:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:51.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.01
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.62
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.69
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.17
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:00.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:55.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:00.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   49.87
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:59.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.08
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:23.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:18.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.56
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.65
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17568.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:00:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.80
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.10
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.28
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.44
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   31.02
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:39.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.80
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   37.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.99
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.22
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:38.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.30
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.58
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  507.77
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  111.99
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   57.45
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.99
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.56
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  526.81
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.65
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.18
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.97
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.20
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5006.94
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.74
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.67
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  340.64
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4974.22
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.57
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  194.77
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.61
p-value of test                       :    0.88


-----------------------------------------------
Normal statistic for number of jumps  :   -0.69
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.08
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:02:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.84
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.60
p-value of test                       :  4.6e-3

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.15
p-value of test                       :    0.9986

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 6.90e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:45.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.54e-3
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.50
p-value of test                       :    0.30

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.59
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.29
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:08.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9891.24
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9850.32
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.96
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.62
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.72
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:04:33.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4992.44
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4883.98
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:56.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4306.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:23.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3988.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12036.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:34.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11927.04
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:37.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.88
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  7999972521

Normal statistic for number of bits   :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   60.54
p-value of test                       :    0.25


-----------------------------------------------
Total number of bits:  8000032278

Normal statistic for number of bits   :    0.26
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.30
p-value of test                       :    0.38

Sample variance                       :    1.37
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:21.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.48
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    1.78
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    0.92
p-value of test                       :    0.18

Sample variance                       :    1.63
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:54.29

 All tests were passed




Server wird beendet - Lösche Semaphor 43745292.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:46.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:15.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:21.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1287
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334407
  j =  1                              :        599997426
  j =  2                              :             1287
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5527
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4462
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:01:40.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:40.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7310
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:11.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7140
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:03:10.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7316
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:04:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7443
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.32
p-value of test                       :    0.92


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.49
p-value of test                       :    0.75

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     873
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.33
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.32
p-value of test                       :    0.93

Test on the Nm values of W_{n,i}(mNP1):    1.75
p-value of test                       :    0.13

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     620
p-value of test                       :    0.21

Stat. AD (mNP2)                       :    0.38
p-value of test                       :    0.87

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.26
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:15.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.33
p-value of test                       :    0.22


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     135
p-value of test                       :    0.88

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:02:45.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   14.59
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.20
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.18
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:59.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.85
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.63
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:11.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.20
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   83.94
p-value of test                       :  5.6e-3

-----------------------------------------------
CPU time used                    :  00:01:26.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.21
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  186.97
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:31.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  394.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1501.53
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:02.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6845.90
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.65
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   64.53
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:03:12.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.80
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:47.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  128.60
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:41.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4989.94
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:01:26.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45559
p-value of test                       :    0.93


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869559
  j =  1                              :        399908885
  j =  2                              :            45553
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46097
p-value of test                       :    0.16


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870097
  j =  1                              :        399907813
  j =  2                              :            46083
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:54.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.36


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:11.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.020
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:39.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-5
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    : 9.21e-5
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.74e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 9.86e-5
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:24.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.60
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:25.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:25.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:48.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.72
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:48.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.70
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:51.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.09
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:58.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.92
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:53.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.89
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   48.49
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.51
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.72
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.38
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:04.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.73
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:29.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.74
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:29.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:19.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.35
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:08.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.61
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:44.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17697.80
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:00:54.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.34
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.09
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.52
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.11
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.62
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.57
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   13.20
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.44
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.81
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.59
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.53
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  484.23
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  159.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.44
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.18
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.33
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  476.39
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.61
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.76
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:44.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.97
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.41
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4983.22
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.48
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  197.05
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.50
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.78
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5223.84
p-value of test                       :    0.01


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.95
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.40
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.34
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.20
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:02:28.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.43
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :    0.16
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:02:27.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.58
p-value of test                       :    0.72

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.26e-3
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 8.20e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.39
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.77
p-value of test                       :    0.16

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  234.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  226.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:06.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9798.31
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.34
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.66
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:13.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.98
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:10.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:04:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4756.26
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:53.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4177.61
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4265.31
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:25.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11620.96
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:34.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11552.81
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.81
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  8000067876

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:02.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.86
p-value of test                       :    0.52


-----------------------------------------------
Total number of bits:  7999966251

Normal statistic for number of bits   :   -0.27
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:02.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.43
p-value of test                       :    0.92

Sample variance                       :    0.89
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:19.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.11
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:22.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:24.65

 All tests were passed




Server wird beendet - Lösche Semaphor 44892172.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:44.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:52.81

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:39.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.32

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1438
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334558
  j =  1                              :        599997124
  j =  2                              :             1438
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:09.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1431
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334551
  j =  1                              :        599997138
  j =  2                              :             1431
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5389
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4385
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:41.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:41.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4367
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7380
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7446
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:03:12.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:04:09.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7149
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.60
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    1.11
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:49.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.68
p-value of test                       :    0.57


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.87
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    1.37
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.48
p-value of test                       :    0.77

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.17
p-value of test                       :    0.9959

-----------------------------------------------
CPU time used                    :  00:02:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.51
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     164
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:02:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.95
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.25
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:11.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.24
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    6.44
p-value of test                       :    0.9941

-----------------------------------------------
CPU time used                    :  00:01:17.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.73
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:11.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.37
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.20
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.08
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.98
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  435.64
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1403.11
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:01.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6995.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.76
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:19.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.40
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:14.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.08
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:47.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  102.62
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:01:43.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5038.74
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:32.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:52.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45635
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869635
  j =  1                              :        399908733
  j =  2                              :            45629
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:47.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45901
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869901
  j =  1                              :        399908201
  j =  2                              :            45895
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:54.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.78e-4
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    : 8.79e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.06e-4
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:24.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:50.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.01
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:52.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.72
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:51.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.65
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.77
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.09
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:51.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.72
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.60
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.80
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.74
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.41
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:28.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.21
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:28.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:18.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.37
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:09.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.81
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17312.39
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.87
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.41
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.61
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.15
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.72
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:38.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.57
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.50
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   24.98
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.08
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.10
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.97
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.10
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   87.82
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.71
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.49
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  490.20
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  127.89
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   49.58
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:44.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  395.49
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.26
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4942.43
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  439.46
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  165.69
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  373.94
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  341.28
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4798.01
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  357.85
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.22
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.67
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.53
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:02:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.30
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.52
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -0.89
p-value of test                       :    0.81

Sample variance                       :    1.69
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:07.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:46.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 2.29e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:45.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.65
p-value of test                       :    0.79

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:39.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.92
p-value of test                       :    0.86

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.9914

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:27.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  184.45
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10018.52
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10072.90
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.93
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:04:36.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.05
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4981.28
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:50.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5038.36
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:53.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.04
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:21.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4026.43
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11919.79
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:31.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11661.40
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:33.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.80
p-value of test                       :    0.37


-----------------------------------------------
Total number of bits:  8000015556

Normal statistic for number of bits   :    0.12
p-value of test                       :    0.45



-----------------------------------------------
CPU time used                    :  00:01:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.65
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  7999988763

Normal statistic for number of bits   :  -0.089
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:01:12.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.53
p-value of test                       :    0.30

Sample variance                       :    0.89
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:33.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.21
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.88
p-value of test                       :    0.81

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:27.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:19.39

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:13.26

 All tests were passed




Server wird beendet - Lösche Semaphor 46039052.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:00:39.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:48.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:30.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:54.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1419
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334539
  j =  1                              :        599997162
  j =  2                              :             1419
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:35.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1314
p-value of test                       :    0.91

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334434
  j =  1                              :        599997372
  j =  2                              :             1314
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1447
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334567
  j =  1                              :        599997106
  j =  2                              :             1447
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5353
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:03:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:45.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4254
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4358
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7253
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7306
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7227
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:17.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.52
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:50.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.87

Test on the Nm values of W_{n,i}(mNP1):    4.91
p-value of test                       :  3.2e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     636
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.73


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     265
p-value of test                       :    0.98

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.76
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     173
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    2.43
p-value of test                       :    0.05

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:49.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.94
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.06
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.30
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.12
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:31.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.26
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.05
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.25
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   42.89
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:24.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  231.26
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:31.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  430.64
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1346.74
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7054.76
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:02.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    2.27
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   48.14
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:20.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.46
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:14.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.96
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:49.64

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.95
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5086.28
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:28.05

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:57.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45859
p-value of test                       :    0.54


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869859
  j =  1                              :        399908284
  j =  2                              :            45855
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.21

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45904
p-value of test                       :    0.46


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869904
  j =  1                              :        399908198
  j =  2                              :            45892
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:30.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.23


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.71


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:11.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:58.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:20.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.55e-4
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:24.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.29e-4
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    : 8.91e-5
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    2.35
p-value of test                       :  9.3e-3

-----------------------------------------------
CPU time used                    :  00:00:24.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.52
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:50.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.44
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   64.25
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.37
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:00:51.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.89
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.86
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.07
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.60
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.03
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.00
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:18.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  160.10
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17515.37
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.55
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   32.41
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.40
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    7.68
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:38.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   20.28
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.89
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.26
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.44
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:38.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.29
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.15
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  462.77
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  157.17
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   79.56
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.85
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.72
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  465.97
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.60
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   99.40
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.62
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.13
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5070.85
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  372.24
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.19
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:36.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.76
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.26
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5218.61
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  166.87
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.19
p-value of test                       :    0.60


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.24
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :    0.97
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:02:23.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.65
p-value of test                       :    0.26

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:19.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.98
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :    1.38
p-value of test                       :    0.08

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:10.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.54e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:45.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.88
p-value of test                       :    0.45

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:33.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.56
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:33.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  219.22
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:13.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9968.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:00.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.84
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4755.16
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4922.08
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4190.25
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3984.17
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12151.39
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11834.08
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.68
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000044548

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:16.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.72
p-value of test                       :    0.95


-----------------------------------------------
Total number of bits:  7999993068

Normal statistic for number of bits   :  -0.055
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:01:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:33.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    3.75
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :    2.11
p-value of test                       :    0.02

Sample variance                       :    2.08
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       : 1 -  8.3e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.58
p-value of test                       :  4.9e-3

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:33.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :    0.18
p-value of test                       :    0.43

Sample variance                       :    0.82
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:39.87

 All tests were passed




Server wird beendet - Lösche Semaphor 47153164.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  9.4e-3


-----------------------------------------------
CPU time used                    :  00:00:49.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.74

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1254
p-value of test                       :    0.9987

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334374
  j =  1                              :        599997492
  j =  2                              :             1254
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1343
p-value of test                       :    0.71

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334463
  j =  1                              :        599997314
  j =  2                              :             1343
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5497
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:57.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7393
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4238
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7449
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:13.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:13.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:04:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7232
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:04:10.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.20
p-value of test                       :    0.9911


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.07
p-value of test                       :    0.08

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     868
p-value of test                       :    0.85

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:49.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     596
p-value of test                       :    0.55

Stat. AD (mNP2)                       :    0.77
p-value of test                       :    0.50

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.27
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:16.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.67
p-value of test                       :    0.58


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.81

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.56
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.09
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:05.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    9.86
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:59.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.22
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:09.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.57
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:09.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.08
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.33
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   78.69
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.18
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.27
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1406.00
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6921.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.25
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   69.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:03:08.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.16
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:45.21

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  106.60
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4887.18
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:13.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46040
p-value of test                       :    0.23


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870040
  j =  1                              :        399907924
  j =  2                              :            46032
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.61

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:33.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.09


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.19
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:46.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:08.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:56.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:37.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.13e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.02e-5
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    : 2.91e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.078
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:46.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.38
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:47.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.86
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:57.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.25
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.64
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.47
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:57.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 1.75e-3
p-value of test                       :    0.9982

Anderson-Darling statistic = A2       :    2.43
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   23.54
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:04.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.99
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.54
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.79
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.69
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  146.62
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:39.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17308.95
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   42.54
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   36.87
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.44
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    5.17
p-value of test                       :    0.9973


-----------------------------------------------
CPU time used                    :  00:00:38.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.28
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.52
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.04
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.71
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:37.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.54
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.33
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  530.18
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.34
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.81
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:44.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.58
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.98
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  495.28
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.96
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.24
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  384.74
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4871.41
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  339.15
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  167.13
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  390.30
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  345.51
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5015.78
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.64
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  163.87
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:00:35.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   23.33
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    2.19
p-value of test                       :    0.01



-----------------------------------------------
CPU time used                    :  00:02:22.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.62
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :    1.89
p-value of test                       :    0.03



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.88
p-value of test                       :    0.97

Sample variance                       :    1.35
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:06.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.17
p-value of test                       :    0.57

Sample variance                       :    1.83
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.51e-3
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    : 3.00e-3
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.26
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.75
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.064
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  173.86
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:01.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.40
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.26
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9913.56
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:01.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.97
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:03:56.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4805.27
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4843.99
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:50.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3968.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4069.43
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11544.07
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11736.56
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:30.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   65.59
p-value of test                       :    0.13


-----------------------------------------------
Total number of bits:  7999978092

Normal statistic for number of bits   :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.49
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000145831

Normal statistic for number of bits   :    1.15
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:04.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9933

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.19
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:10.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Tests on the sum of all N observations
Standardized normal statistic         :   -0.24
p-value of test                       :    0.60

Sample variance                       :    1.95
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :    0.27
p-value of test                       :    0.39

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:22.97

 All tests were passed




Server wird beendet - Lösche Semaphor 48201740.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:38.52

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:49.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.35

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1420
p-value of test                       :    0.07

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334540
  j =  1                              :        599997160
  j =  2                              :             1420
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5470
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:03:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:42.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7333
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4438
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4324
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7282
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7337
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:05.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7194
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:07.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.39


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.57
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    2.74
p-value of test                       :    0.04

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     862
p-value of test                       :    0.89

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     618
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:15.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.73
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    1.50
p-value of test                       :    0.18

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     335
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:17.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.14
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.88
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:46.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.74
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   30.05
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.22
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:10.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.96
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:11.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.60
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:22.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.68
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  422.32
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:47.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1423.40
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:03.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6857.45
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:49.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.43
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:08.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.94
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:44.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.84
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:01:36.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4959.52
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:57.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908296
  j =  2                              :            45849
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.13

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45711
p-value of test                       :    0.78


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869711
  j =  1                              :        399908581
  j =  2                              :            45705
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.42


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:32.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.75
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:19.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.73
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.01


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :  6.9e-3

Kolmogorov-Smirnov- statistic = D-    : 6.80e-3
p-value of test                       :    0.9923

Anderson-Darling statistic = A2       :    3.49
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:52.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:02:06.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:58.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:20.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.04e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 4.59e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:23.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.57e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:24.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.42
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.53
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.85
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:49.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.19
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:56.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.74
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.19
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:47.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.85
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:56.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.97
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:57.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.33
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:45.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.24
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   56.28
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:05.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :   13.42
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:28.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.07
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:28.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.45
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  149.60
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:39.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17480.69
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   62.00
p-value of test                       :  3.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.89
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.36
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.11
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.82
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.05
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.75
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.28
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   25.23
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:38.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.78
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.96
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  455.86
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.51
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.00
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.31
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.79
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  468.54
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.50
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   82.45
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:00:44.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.41
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.76
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5018.20
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  366.43
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  221.87
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:35.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  421.39
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.37
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5031.53
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.74
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.83
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.28
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :    0.37
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:02:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.64
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -1.74
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:02:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.16
p-value of test                       :    0.12

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -0.90
p-value of test                       :    0.82

Sample variance                       :    1.43
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:06.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.14e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:45.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.65e-3
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    : 8.33e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.98
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.70
p-value of test                       :    0.29

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.05
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  204.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9910.81
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:59.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10078.34
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:59.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.31
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:59.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.16
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:00.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.75
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:03:57.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.11
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:50.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    3.05
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4664.44
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4093.91
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4104.33
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:24.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11876.83
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:29.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11805.31
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:30.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.98
p-value of test                       :    0.67


-----------------------------------------------
Total number of bits:  7999926096

Normal statistic for number of bits   :   -0.58
p-value of test                       :    0.72



-----------------------------------------------
CPU time used                    :  00:01:03.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   42.86
p-value of test                       :    0.86


-----------------------------------------------
Total number of bits:  8000031990

Normal statistic for number of bits   :    0.25
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Tests on the sum of all N observations
Standardized normal statistic         :    0.25
p-value of test                       :    0.40

Sample variance                       :    1.56
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:22.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   0.091
p-value of test                       :    0.46

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.88
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    1.94
p-value of test                       :    0.03

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.93

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:21.25

 All tests were passed




Server wird beendet - Lösche Semaphor 49250316.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:38.49

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1418
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334538
  j =  1                              :        599997164
  j =  2                              :             1418
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1445
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334565
  j =  1                              :        599997110
  j =  2                              :             1445
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.84

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5430
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7418
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:44.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7109
p-value of test                       :    0.9929


-----------------------------------------------
CPU time used                    :  00:03:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7273
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:04:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7195
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:10.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.37
p-value of test                       :    0.88

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     911
p-value of test                       :    0.36

Stat. AD (mNP2)                       :    0.98
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.21
p-value of test                       :    0.26


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.24
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     595
p-value of test                       :    0.57

Stat. AD (mNP2)                       :    1.06
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:14.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.24
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.23
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     317
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    1.41
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.93
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.95
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     139
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:46.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.59
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.66
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.30
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.12
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:11.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:21.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   57.69
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:22.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.45
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.24
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  438.46
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1349.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6945.78
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:50.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.63
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:16.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:09.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.19
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:45.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  133.78
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:36.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4986.97
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:03:00.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45976
p-value of test                       :    0.33


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869976
  j =  1                              :        399908050
  j =  2                              :            45972
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.22

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45876
p-value of test                       :    0.51


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869876
  j =  1                              :        399908250
  j =  2                              :            45872
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.28
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:30.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:19.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.15


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:01:48.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:07.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.87e-4
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    : 1.38e-4
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.19e-4
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 1.02e-4
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:48.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.15
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.63
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:50.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   16.61
p-value of test                       :    0.9985

-----------------------------------------------
CPU time used                    :  00:00:57.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.39
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.34
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.47
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.45
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.95
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:28.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.24
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:27.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:18.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:08.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  116.81
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.59
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.89
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.52
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.17
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.60
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.85
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:37.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.64
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.32
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   39.30
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.76
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.86
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:00:37.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.88
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  171.50
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.09
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.04
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  110.95
p-value of test                       :  3.5e-3


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.76
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.14
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.92
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.69
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.30
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.33
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.55
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5157.10
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.86
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.80
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  441.63
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.36
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5196.48
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.20
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.02
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:35.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.67
p-value of test                       :    0.93


-----------------------------------------------
Normal statistic for number of jumps  :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.44
p-value of test                       :    0.22


-----------------------------------------------
Normal statistic for number of jumps  :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:02:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.28
p-value of test                       :    0.39

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.56
p-value of test                       :    0.06

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:07.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.16e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 9.00e-3
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.23e-3
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:43.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.97
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.82
p-value of test                       :    0.87

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  212.39
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:02:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  228.90
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.00e-3
p-value of test                       :    0.9980

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10260.31
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:59.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9942.26
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:02.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    2.55
p-value of test                       :  5.4e-3

-----------------------------------------------
CPU time used                    :  00:01:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.42
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:04:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4956.69
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.77
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4227.03
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4244.15
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11982.71
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:29.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11646.71
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:30.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.33
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000040846

Normal statistic for number of bits   :    0.32
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:04.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.81
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000116125

Normal statistic for number of bits   :    0.92
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.45

Sample variance                       :    0.88
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:21.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.09
p-value of test                       :    0.86

Sample variance                       :    1.37
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:09.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.02
p-value of test                       :    0.15

Sample variance                       :    1.54
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.43

Sample variance                       :    1.27
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:41.46

 All tests were passed




Server wird beendet - Lösche Semaphor 50298892.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:39.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:48.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:32.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:55.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:10.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1282
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334402
  j =  1                              :        599997436
  j =  2                              :             1282
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5329
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:58.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7376
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:02:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4234
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7349
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7385
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:13.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:13.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.42


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    0.44
p-value of test                       :    0.80

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    1.23
p-value of test                       :    0.26

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:50.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.24
p-value of test                       :    0.25


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    1.53
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     584
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    3.99
p-value of test                       :  8.8e-3

-----------------------------------------------
CPU time used                    :  00:01:16.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.17
p-value of test                       :    0.28


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.32
p-value of test                       :  6.4e-3

Test on the Nm values of W_{n,i}(mNP1):    0.21
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.64
p-value of test                       :    0.61

Stat. AD after spacings (mNP2-S)      :    0.20
p-value of test                       :    0.9904

-----------------------------------------------
CPU time used                    :  00:02:16.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.48
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.53

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.31

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.15
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:08.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.79
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.21
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:13.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.39
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.27
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.14
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.95
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:23.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  252.09
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.31
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:55.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1534.47
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6977.92
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:58.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   37.13
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:19.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   41.37
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.56
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:47.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  161.41
p-value of test                       :  5.9e-3


-----------------------------------------------
CPU time used                    :  00:01:40.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5006.21
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:01:26.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45785
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869785
  j =  1                              :        399908433
  j =  2                              :            45779
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.94

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45865
p-value of test                       :    0.53


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869865
  j =  1                              :        399908272
  j =  2                              :            45861
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.10


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:02:30.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.25


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.31


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:02:08.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:57.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:20.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:38.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.72e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 5.54e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.95e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.16
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.81
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   46.84
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:58.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.13
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:59.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.13
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:51.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.63
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.27
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   26.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:52.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.47
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:04.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.05
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.28
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:27.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.63
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:27.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:17.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.67
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  103.43
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17207.83
p-value of test                       :    0.88



-----------------------------------------------
CPU time used                    :  00:00:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.68
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.96
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.31
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.85
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.97
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:37.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.66
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.98
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   14.08
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.31
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.14
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:37.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.24
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  540.74
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  115.65
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.25
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:44.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  185.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.28
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  122.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.27
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  337.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5026.86
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  364.22
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.02
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.59
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.49
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5008.53
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  337.33
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  199.08
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.49
p-value of test                       :    0.57


-----------------------------------------------
Normal statistic for number of jumps  :    0.68
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:02:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.74
p-value of test                       :    0.39


-----------------------------------------------
Normal statistic for number of jumps  :   -0.77
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.67
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.02e-3
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 7.09e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 8.53e-3
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.55
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.37
p-value of test                       :    0.82

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.41
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.036
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.23
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  161.38
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:07.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.06
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  233.85
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.92
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9857.24
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.60
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:08.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:04:20.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4948.50
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:01.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3911.45
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:26.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4230.06
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:29.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11887.66
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:36.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11582.96
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:38.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.15
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000006958

Normal statistic for number of bits   :   0.055
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:01:05.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   43.67
p-value of test                       :    0.84


-----------------------------------------------
Total number of bits:  8000066376

Normal statistic for number of bits   :    0.52
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.64
p-value of test                       :    0.26

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.71
p-value of test                       :    0.96

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.84
p-value of test                       :    0.20

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:25.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:03.04

 All tests were passed




Server wird beendet - Lösche Semaphor 51347468.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:39.96

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:33.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1456
p-value of test                       :  7.2e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334576
  j =  1                              :        599997088
  j =  2                              :             1456
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5411
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:02:45.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4248
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4425
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:04.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7252
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:03:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7365
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:15.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7221
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:04:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:04:12.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.84


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.22
p-value of test                       :    0.07

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     927
p-value of test                       :    0.19

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.86


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.35

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    1.39
p-value of test                       :    0.21

Stat. AD after spacings (mNP2-S)      :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.44
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     312
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.97
p-value of test                       :    0.37

Stat. AD after spacings (mNP2-S)      :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:02:16.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.88
p-value of test                       :    0.42

Test on the Nm values of W_{n,i}(mNP1):    1.14
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.48
p-value of test                       :    0.76

Stat. AD after spacings (mNP2-S)      :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:02:45.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.02
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:08.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.34
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:59.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.63
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:14.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   72.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.44
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   81.39
p-value of test                       :  9.4e-3

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  241.36
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:31.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.90
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1554.94
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:05.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7125.00
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:02:00.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.65
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   65.02
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:15.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.89
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:47.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  101.91
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:43.43

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5019.78
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:30.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:59.09

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45742
p-value of test                       :    0.74


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869742
  j =  1                              :        399908517
  j =  2                              :            45740
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45769
p-value of test                       :    0.70


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869769
  j =  1                              :        399908465
  j =  2                              :            45763
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    : 4.96e-3
p-value of test                       :    0.9940

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.74
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.91


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:21.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:53.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:10.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.38e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 1.72e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.77e-4
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 7.81e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.78
p-value of test                       :  2.7e-3

-----------------------------------------------
CPU time used                    :  00:00:25.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.11
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:43.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.060
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:44.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.72
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:52.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.42
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:01.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.93
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:02.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.50
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:51.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.69
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.90
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.85
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:55.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.75e-4
p-value of test                       :    0.9992    *****

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    3.24
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   70.07
p-value of test                       :  2.3e-3

-----------------------------------------------
CPU time used                    :  00:01:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.32
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:02.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.90
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.45
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.22
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:07.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.50
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17359.93
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:00:53.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.63
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.35
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.88
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.55
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:36.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.17
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.78
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:36.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.69
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  473.05
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.29
p-value of test                       :    0.9906


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.66
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  161.25
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.29
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.76
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.94
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   83.78
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:43.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.74
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.74
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4810.86
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  305.24
p-value of test                       :    0.9975


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.31
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:35.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  401.32
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.48
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5035.51
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.80
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  190.27
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.64
p-value of test                       :    0.26


-----------------------------------------------
Normal statistic for number of jumps  :   -0.72
p-value of test                       :    0.76



-----------------------------------------------
CPU time used                    :  00:02:19.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.38
p-value of test                       :    0.42


-----------------------------------------------
Normal statistic for number of jumps  :   0.052
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:20.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.48
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.53
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:01.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Tests on the sum of all N observations
Standardized normal statistic         :   -0.84
p-value of test                       :    0.80

Sample variance                       :    0.98
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:04.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.78e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:42.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    1.31
p-value of test                       :    0.9954

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:31.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.53
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:32.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:20.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  195.74
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:22.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.17
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:57.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9988.91
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:14.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.26
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.055
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:41.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.22
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:50.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4767.52
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4206.29
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4132.64
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:23.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11978.43
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:32.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12334.18
p-value of test                       :  5.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:34.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.43
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  7999922586

Normal statistic for number of bits   :   -0.61
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.49
p-value of test                       :    0.35


-----------------------------------------------
Total number of bits:  7999981245

Normal statistic for number of bits   :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:01:19.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :   -1.11
p-value of test                       :    0.87

Sample variance                       :    0.64
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.74
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :    1.68
p-value of test                       :    0.05

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:22.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    1.01
p-value of test                       :    0.16

Sample variance                       :    0.54
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.13
p-value of test                       :    0.9995    *****

Tests on the sum of all N observations
Standardized normal statistic         :   0.028
p-value of test                       :    0.49

Sample variance                       :    0.92
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:23.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:13.00
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 100  HammingIndep, L=1200, r=25      5.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52396044.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:40.20

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:49.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1320
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334440
  j =  1                              :        599997360
  j =  2                              :             1320
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1434
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334554
  j =  1                              :        599997132
  j =  2                              :             1434
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5504
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:04:12.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4237
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:50.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:00.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4292
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:02:20.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4260
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:20.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:03:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:43.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:05:14.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7426
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:05:16.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.34

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     967
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:49.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.47
p-value of test                       :    0.78

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.96

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     581
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    0.51
p-value of test                       :    0.74

Stat. AD after spacings (mNP2-S)      :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:15.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.54

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     300
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.78
p-value of test                       :    0.49


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.19
p-value of test                       :    0.9919

Stat. AD after spacings (mNP2-S)      :    1.78
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:02:46.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.47
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.02
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:05.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.96
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:58.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.96
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   68.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:12.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.16
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:21.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.98
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.55
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  207.39
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:49.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.23
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:02:00.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7241.49
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:51.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.67
p-value of test                       :  4.7e-3

Kolmogorov-Smirnov- statistic = D-    : 5.35e-3
p-value of test                       :    0.9945

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.5e-3

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   12.31
p-value of test                       :    0.9982

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :  8.6e-3

Anderson-Darling statistic = A2       :    3.46
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   84.24
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.25
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:00:45.63

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  116.42
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:38.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4957.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:13.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.64e+6
p-value of test                       :  9.7e-3


-----------------------------------------------
CPU time used                    :  00:02:59.47

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46055
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870055
  j =  1                              :        399907894
  j =  2                              :            46047
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45293
p-value of test                       :    0.9969


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869293
  j =  1                              :        399909418
  j =  2                              :            45285
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:33.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.90


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:24.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.51


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:57.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.025
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.93e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 3.12e-5
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.21e-4
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.35
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.24
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.035
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.88
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   48.55
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:00.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.98
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:18.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.02
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.99
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:59.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   44.24
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:19.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.55
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:19.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.63
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.19
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:10.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.14
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.96
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:26.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.68
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:25.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.19
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  138.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17555.80
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:00:52.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.05
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   27.29
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.66
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.83
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.21
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:36.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.55
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   46.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.33
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   36.29
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.71
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.18
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.05
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.83
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.72
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.56
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  169.07
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.85
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.47
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.95
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.72
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:41.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.49
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  383.84
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4815.31
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  394.96
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.50
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:34.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.46
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.61
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4792.25
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  378.77
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.72
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:34.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.10
p-value of test                       :    0.44


-----------------------------------------------
Normal statistic for number of jumps  :    0.81
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:20.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   22.72
p-value of test                       :    0.03


-----------------------------------------------
Normal statistic for number of jumps  :    0.48
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:19.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.63
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.11

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    : 8.35e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.07e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 6.25e-3
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:43.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.27
p-value of test                       :    0.08

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.98
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.35
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.28
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10071.64
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:58.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9885.90
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.34
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.30
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:04:07.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4840.96
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:51.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4947.88
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:52.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4138.97
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:22.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4033.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11842.46
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:30.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11561.36
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:30.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.59
p-value of test                       :    0.75


-----------------------------------------------
Total number of bits:  8000041725

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   35.71
p-value of test                       :    0.97


-----------------------------------------------
Total number of bits:  8000021961

Normal statistic for number of bits   :    0.17
p-value of test                       :    0.43



-----------------------------------------------
CPU time used                    :  00:01:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:24.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.41
p-value of test                       :    0.34

Sample variance                       :    0.44
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:13.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.29

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    1.05
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:12.01

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:13:47.01

 All tests were passed




Server wird beendet - Lösche Semaphor 53444620.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:38.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1399
p-value of test                       :    0.18

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334519
  j =  1                              :        599997202
  j =  2                              :             1399
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5540
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:00.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:43.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7417
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:45.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:00.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7406
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:12.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7301
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:04:08.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:04:14.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.66
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.26
p-value of test                       :    0.97

Test on the Nm values of W_{n,i}(mNP1):    2.25
p-value of test                       :    0.07

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     942
p-value of test                       :    0.08

Stat. AD (mNP2)                       :    0.86
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    1.96
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:49.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.02
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.08
p-value of test                       :    0.32


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    4.43
p-value of test                       :  5.7e-3

Test on the Nm values of W_{n,i}(mNP1):    2.51
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     276
p-value of test                       :    0.91

Stat. AD (mNP2)                       :    0.35
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:17.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.46
p-value of test                       :    0.78


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.72
p-value of test                       :    0.55

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.82
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:54.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.04
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.76
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.88
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.67
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:22.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.99
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:21.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   40.98
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:27.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.27
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1366.28
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6917.90
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:53.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   29.17
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:20.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   46.43
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:03:10.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.74
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:48.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  124.47
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:01:39.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5010.34
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:30.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:05.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45980
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869980
  j =  1                              :        399908044
  j =  2                              :            45972
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.52

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46099
p-value of test                       :    0.15


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870099
  j =  1                              :        399907805
  j =  2                              :            46093
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:02:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:02:26.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.66


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:00.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.70


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:17.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :  1.0e-2

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:57.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:20.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:39.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 1.16e-4
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.45e-4
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 6.65e-5
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:24.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.60
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:23.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:23.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:39.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:40.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   90.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:52.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.62
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.03
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.57
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.33
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   32.31
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:54.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.53
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:01.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.92
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.64
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.81
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.93
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:14.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:06.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  119.87
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:44.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17334.90
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.96
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.20
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   38.12
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   23.25
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   30.81
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   55.21
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   48.91
p-value of test                       :  2.9e-3


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.23
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.64
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  159.38
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.21
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  548.97
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  144.38
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.78
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.35
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.17
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  543.29
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  129.45
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.11
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:42.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.45
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5001.14
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.19
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  220.99
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.31
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  415.60
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.99
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.90
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  198.11
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:00:34.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.53
p-value of test                       :    0.33


-----------------------------------------------
Normal statistic for number of jumps  :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   25.62
p-value of test                       :    0.01


-----------------------------------------------
Normal statistic for number of jumps  :   -1.01
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:19.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    2.63
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.77
p-value of test                       :    0.96

Sample variance                       :    1.92
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:01.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:03.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:43.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 9.54e-3
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:43.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.42
p-value of test                       :    0.39

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.51
p-value of test                       :    0.81

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  213.80
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:02.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  207.24
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:02.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10200.79
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10201.35
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.33
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:11.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.01
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:08.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:04:35.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    1.66
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4726.01
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4972.74
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:57.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4047.06
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:24.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4025.92
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:26.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11605.89
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:34.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12088.02
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:33.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.54
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999875222

Normal statistic for number of bits   :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:01:11.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.87
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999839804

Normal statistic for number of bits   :   -1.27
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.28
p-value of test                       :    0.90

Sample variance                       :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:18.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    4.38
p-value of test                       :  6.0e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.78
p-value of test                       :    0.9973

Sample variance                       :    1.28
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:25.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Tests on the sum of all N observations
Standardized normal statistic         :    0.58
p-value of test                       :    0.28

Sample variance                       :    1.19
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:20.42

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:48.05

 All tests were passed




Server wird beendet - Lösche Semaphor 54493196.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:40.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:49.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5513
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:59.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:45.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4268
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:00.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4216
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7469
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:10.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7432
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7255
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:04:04.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:04.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    1.62
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:49.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.22

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.36
p-value of test                       :    0.21

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     313
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.52
p-value of test                       :    0.72

Stat. AD after spacings (mNP2-S)      :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:02:15.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.45


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    3.60
p-value of test                       :    0.01

Test on the Nm values of W_{n,i}(mNP1):    0.78
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     141
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    0.81
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:50.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.32
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.43
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.32
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.89
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.48
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:09.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.06
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.13
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  230.69
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  444.28
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1408.47
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:01.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7184.84
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:53.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.54
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:14.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   62.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:03:12.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.51
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:44.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  113.02
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:36.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4970.91
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:14.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.62e+6
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:03:23.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45490
p-value of test                       :    0.97


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869490
  j =  1                              :        399909026
  j =  2                              :            45478
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45922
p-value of test                       :    0.42


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869922
  j =  1                              :        399908161
  j =  2                              :            45912
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:07.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:02:33.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.045
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.018
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.26


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:37.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.49e-4
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 1.83e-4
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.67e-5
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    : 2.35e-4
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:40.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.81
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.39
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:55.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.79
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:55.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.00
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:54.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.09
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.15
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:45.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.62
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   58.93
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:02.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:02.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.10
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.56
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:25.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.23
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:38.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17260.42
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:00:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   45.74
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.35
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.06
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.03
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.66
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.91
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.34
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.85
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.88
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.13
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.46
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.01
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  148.28
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   91.33
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.59
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.96
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  430.70
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :   98.13
p-value of test                       :    0.9940


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.66
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:42.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  409.17
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  410.43
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4973.01
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  417.55
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  154.37
p-value of test                       :    0.9928


-----------------------------------------------
CPU time used                    :  00:00:34.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  423.30
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.85
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.35
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  409.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.13
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.84
p-value of test                       :    0.25


-----------------------------------------------
Normal statistic for number of jumps  :    0.80
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:02:18.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.63
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :    0.75
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:02:19.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.08
p-value of test                       :    0.14

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    0.36
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:03.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    : 4.95e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    : 9.12e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:43.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.88
p-value of test                       :    0.77

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.39
p-value of test                       :    0.49

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.84e-3
p-value of test                       :    0.9971

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  162.16
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  237.69
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:02:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10036.18
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9832.81
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:01.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -2.54
p-value of test                       :    0.9945

-----------------------------------------------
CPU time used                    :  00:01:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -2.18
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:02.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.68
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:04:11.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4866.42
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:52.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4898.34
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:54.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4082.90
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:23.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4090.16
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:24.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11921.95
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11607.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   72.06
p-value of test                       :    0.05


-----------------------------------------------
Total number of bits:  7999775817

Normal statistic for number of bits   :   -1.77
p-value of test                       :    0.96



-----------------------------------------------
CPU time used                    :  00:01:04.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.19
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999999563

Normal statistic for number of bits   : -3.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:05.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    1.65
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.59
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:13.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.23
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -0.62
p-value of test                       :    0.73

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.44
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:13.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:56.87

 All tests were passed




Server wird beendet - Lösche Semaphor 55541772.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:40.14

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:49.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:56.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1440
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334560
  j =  1                              :        599997120
  j =  2                              :             1440
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1267
p-value of test                       :    0.9959

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334387
  j =  1                              :        599997466
  j =  2                              :             1267
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5328
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:04:00.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4514
p-value of test                       :  3.8e-3


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7289
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:45.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4327
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7254
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:03:11.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7421
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:03:11.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:04:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.72
p-value of test                       :    0.54


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.29

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     937
p-value of test                       :    0.11

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    1.34
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.47
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.49
p-value of test                       :    0.18

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     612
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.90
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     294
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.74
p-value of test                       :    0.53

Stat. AD after spacings (mNP2-S)      :    0.71
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:02:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     151
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.44
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    0.89
p-value of test                       :    0.9964

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.85
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.46
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.16
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:08.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.34
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.51
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:21.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  264.92
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  414.87
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:51.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1519.16
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:02:01.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7161.02
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:51.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.09
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    3.88
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   89.63
p-value of test                       :  7.9e-3

-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.83
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:45.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  152.70
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:37.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5309.48
p-value of test                       :  4.0e-3


-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:03:19.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907767
  j =  2                              :            46112
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:57.01

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46166
p-value of test                       :    0.09


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870166
  j =  1                              :        399907671
  j =  2                              :            46160
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:05.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.21


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.022
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    2.95
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:33.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.79


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.084
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.78


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.16
p-value of test                       :    0.9978

-----------------------------------------------
CPU time used                    :  00:01:18.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:37.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.80e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.98e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.24e-4
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.12
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:00:23.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.70
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.00
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:39.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.26
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   41.47
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   49.41
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.62
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.10
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:51.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.76
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:54.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   23.40
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:45.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.20
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.88
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.37
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.13
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.25
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  134.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:38.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17489.81
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   50.62
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.14
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.35
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.99
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.87
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:36.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.08
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.37
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.49
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.60
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.92
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.69
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.41
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  140.51
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   58.30
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  128.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.17
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  503.61
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.69
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.49
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  408.09
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  347.08
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4833.97
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  402.61
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  182.07
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:34.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.48
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  363.89
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.77
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.65
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.51
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:34.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.23
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -0.90
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:19.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.92
p-value of test                       :    0.38


-----------------------------------------------
Normal statistic for number of jumps  :  -0.100
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:19.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.38
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.57
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :    1.29
p-value of test                       :    0.10

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    : 6.98e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:44.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 7.58e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.01
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:23.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.06
p-value of test                       :    0.93

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:21.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  177.74
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:02:01.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9925

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.00
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.57
p-value of test                       :  6.5e-4    *****

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    3.59
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9749.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10145.86
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:01.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.02
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:00.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:01.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.6e-3

Kolmogorov-Smirnov- statistic = D-    :   0.069
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    4.35
p-value of test                       :  6.2e-3

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4648.53
p-value of test                       :    0.9934

-----------------------------------------------
CPU time used                    :  00:01:51.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4859.46
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:52.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:22.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4019.73
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:25.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12231.34
p-value of test                       :  4.4e-3

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12031.48
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:31.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.85
p-value of test                       :    0.15


-----------------------------------------------
Total number of bits:  8000079012

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:04.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.71
p-value of test                       :    0.34


-----------------------------------------------
Total number of bits:  8000080278

Normal statistic for number of bits   :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:01:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.67
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :   -1.78
p-value of test                       :    0.96

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.32e-3
p-value of test                       :    0.9933

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :    1.83
p-value of test                       :    0.03

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.73
p-value of test                       :    0.23

Sample variance                       :    1.12
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.13
p-value of test                       :    0.45

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.80

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:28.95

 All tests were passed




Server wird beendet - Lösche Semaphor 56590348.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1309
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334429
  j =  1                              :        599997382
  j =  2                              :             1309
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.52

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5390
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4259
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:43.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7276
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:47.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4444
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4277
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:02.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7307
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:03:12.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7367
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:03:12.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7341
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:04:03.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7384
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:04:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.45
p-value of test                       :    0.19


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     876
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:49.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.83
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.95

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     599
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:15.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.09
p-value of test                       :    0.31


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.33
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    3.28
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     344
p-value of test                       :  6.9e-3

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.39

Stat. AD after spacings (mNP2-S)      :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:14.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    3.18
p-value of test                       :    0.02

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    5.42
p-value of test                       :  1.8e-3

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:44.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.45
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   28.38
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:08.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.43
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.29
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.73
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  208.74
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  419.45
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1422.38
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7083.55
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:51.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.04
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   63.40
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:03:10.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.91
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:44.73

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  108.09
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:01:37.09

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5102.09
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:14.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:05.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908211
  j =  2                              :            45887
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.68

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45841
p-value of test                       :    0.57


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869841
  j =  1                              :        399908321
  j =  2                              :            45835
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.036
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    : 4.03e-3
p-value of test                       :    0.9953

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:02:32.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.41


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :   0.081
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.48


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:01:53.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.071
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:13.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.25e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 1.28e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.37e-4
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    : 2.81e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:24.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.046
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:37.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.73
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:36.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   77.84
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   75.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:00:56.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   44.96
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:55.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.80
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.23
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.09
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.11
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.53
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.72
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:24.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.08
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.76
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.23
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:38.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17678.28
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.47
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.65
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.42
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.73
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.10
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:37.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.94
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.46
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   11.62
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.69
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.50
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.82
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  442.09
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.95
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   47.61
p-value of test                       :    0.9927


-----------------------------------------------
CPU time used                    :  00:00:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.42
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.11
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.67
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  120.97
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.15
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:00:42.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.83
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.48
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4953.09
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  353.74
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.08
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:00:34.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.00
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.42
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5019.52
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  345.84
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.62
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:34.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.14
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :    0.31
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   21.75
p-value of test                       :    0.04


-----------------------------------------------
Normal statistic for number of jumps  :    0.63
p-value of test                       :    0.26



-----------------------------------------------
CPU time used                    :  00:02:19.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    2.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:08.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    : 7.62e-3
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:44.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:43.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.11
p-value of test                       :    0.26

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.61
p-value of test                       :    0.80

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.09
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:04.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.82
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:03.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.79
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:58.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.09
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:01.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:01.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:04:04.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4788.63
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:51.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4890.86
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:52.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4174.09
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:22.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4155.95
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:24.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11913.40
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:30.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11609.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:30.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   45.71
p-value of test                       :    0.78


-----------------------------------------------
Total number of bits:  8000097426

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.92
p-value of test                       :    0.63


-----------------------------------------------
Total number of bits:  7999968192

Normal statistic for number of bits   :   -0.25
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:01:05.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :  4.0e-3

Anderson-Darling statistic = A2       :    2.78
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :    1.71
p-value of test                       :    0.04

Sample variance                       :    0.20
p-value of test                       :    0.9940

-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.51
p-value of test                       :    0.31

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:11.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    4.06
p-value of test                       :  3.2e-5    *****

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.03
p-value of test                       :    0.85

Sample variance                       :    1.29
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:16.70

 All tests were passed




Server wird beendet - Lösche Semaphor 57638924.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:38.64

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:49.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1275
p-value of test                       :    0.9923

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334395
  j =  1                              :        599997450
  j =  2                              :             1275
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.85

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1393
p-value of test                       :    0.22

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334513
  j =  1                              :        599997214
  j =  2                              :             1393
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5460
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:04:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:45.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7320
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4485
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4304
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:02:26.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7462
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:03:54.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7168
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:03:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:05:30.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.76
p-value of test                       :    0.51


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    0.70
p-value of test                       :    0.56

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    2.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:49.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.71
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.68

Test on the Nm values of W_{n,i}(mNP1):    0.84
p-value of test                       :    0.45

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     614
p-value of test                       :    0.29

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.88
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.80
p-value of test                       :    0.48

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.62
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.82
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     150
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    0.41
p-value of test                       :    0.84

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:40.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.93
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.54
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:04.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.33
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:57.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.33
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:08.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   52.32
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:09.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.92
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.52
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  248.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.15
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:30.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1385.77
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:02:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6783.61
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:35.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.27
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:14.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.9912

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   83.78
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:03:11.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.33
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:44.93

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.12
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:37.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4861.24
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:01:13.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:02.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45890
p-value of test                       :    0.48


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869890
  j =  1                              :        399908224
  j =  2                              :            45882
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46204
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870204
  j =  1                              :        399907595
  j =  2                              :            46198
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.58


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:26.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:54.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:02:14.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:18.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.03e-4
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    : 1.21e-4
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:23.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.34e-5
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    : 2.27e-4
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:23.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.37
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.25
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:40.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   93.83
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:50.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   65.95
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:38.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   52.24
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.68
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:50.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.78
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.04
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:37.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.70
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.30
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.64
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.86
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:25.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.34
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.47
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:15.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  122.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:38.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17368.25
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:54.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.84
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   16.38
p-value of test                       :    0.9969


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.09
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.14
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.64
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.73
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.74
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.79
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.12
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.90
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.33
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  494.20
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.87
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   84.64
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:43.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.71
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  173.36
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  480.43
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.38
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.56
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:42.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  438.91
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.57
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5207.07
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  400.06
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.41
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  396.09
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.04
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5032.55
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  430.58
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.59
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.21
p-value of test                       :    0.43


-----------------------------------------------
Normal statistic for number of jumps  :    1.30
p-value of test                       :    0.10



-----------------------------------------------
CPU time used                    :  00:02:19.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.62
p-value of test                       :    0.81


-----------------------------------------------
Normal statistic for number of jumps  :   -0.17
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:02:19.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Tests on the sum of all N observations
Standardized normal statistic         :   -0.22
p-value of test                       :    0.59

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    0.78
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:44.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 4.85e-3
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:43.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.61
p-value of test                       :    0.17

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.77
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   37.00
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:01:21.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  183.28
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:03.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  189.18
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:04.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9874.53
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:58.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9829.79
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:01.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.097
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:01.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.012
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:01.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.50
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:04:05.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5060.49
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:51.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4950.70
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:52.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4312.59
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4187.04
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:30.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11885.29
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:30.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.18
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  8000134236

Normal statistic for number of bits   :    1.06
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.24
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  8000097006

Normal statistic for number of bits   :    0.77
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:05.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :    0.67
p-value of test                       :    0.25

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:23.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :   -1.34
p-value of test                       :    0.91

Sample variance                       :    2.25
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :   -0.38
p-value of test                       :    0.65

Sample variance                       :    0.38
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.19
p-value of test                       :    0.57

Sample variance                       :    0.76
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:09.70

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:15:48.34

 All tests were passed




Server wird beendet - Lösche Semaphor 58687500.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :  4.8e-3


-----------------------------------------------
CPU time used                    :  00:00:49.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1368
p-value of test                       :    0.46

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334488
  j =  1                              :        599997264
  j =  2                              :             1368
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1256
p-value of test                       :    0.9984

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334376
  j =  1                              :        599997488
  j =  2                              :             1256
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1351
p-value of test                       :    0.63

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334471
  j =  1                              :        599997298
  j =  2                              :             1351
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5377
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:00.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7354
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:02:46.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:01.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7258
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:14.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7305
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:04:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7244
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.98
p-value of test                       :    0.09

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     929
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    3.02
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.81
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    0.35
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     602
p-value of test                       :    0.47

Stat. AD (mNP2)                       :    1.00
p-value of test                       :    0.36

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:14.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.41
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:02:15.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.80


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.18
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.67

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.26
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.31
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.09
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:59.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    7.49
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:13.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.20
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:08.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.35
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.88
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:22.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.30
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  234.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:29.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.51
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1392.57
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7080.70
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:53.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.77
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.53
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:03:13.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.12
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:00:45.78

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  151.22
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:40.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5022.83
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:01:28.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:03:02.31

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45853
p-value of test                       :    0.55


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869853
  j =  1                              :        399908296
  j =  2                              :            45849
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908120
  j =  2                              :            45934
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:31.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.07
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:52.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:08.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:56.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:38.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.62e-5
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    : 1.65e-4
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.09e-4
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    : 2.65e-5
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    4.49
p-value of test                       :  5.0e-3

-----------------------------------------------
CPU time used                    :  00:00:24.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:24.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:42.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:42.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   84.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:51.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:58.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.64
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:58.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:52.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:00:59.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   50.64
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.95
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.98
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:02.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.97
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:02.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.49
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.35
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:24.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.18
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:15.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.40
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  126.14
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17465.09
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.87
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.21
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.99
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.45
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.04
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   33.22
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.27
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   25.64
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.66
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.13
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.11
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.44
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  130.61
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   75.69
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:43.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.30
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.10
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.67
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  150.37
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   61.24
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.26
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  419.11
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5002.48
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  385.14
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  206.15
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:35.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.26
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.84
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4986.72
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  320.16
p-value of test                       :    0.99


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.38
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.44
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :  -0.028
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:18.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.02
p-value of test                       :    0.78


-----------------------------------------------
Normal statistic for number of jumps  :   -1.43
p-value of test                       :    0.92



-----------------------------------------------
CPU time used                    :  00:02:19.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :    1.20
p-value of test                       :    0.12

Sample variance                       :    0.90
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.80
p-value of test                       :    0.21

Sample variance                       :    0.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 2.13e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.02e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:42.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.06
p-value of test                       :    0.85

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.02
p-value of test                       :    0.65

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:20.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    : 1.14e-3
p-value of test                       :    0.9988

Anderson-Darling statistic = A2       :    4.14
p-value of test                       :  7.8e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  147.05
p-value of test                       :    0.9981

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.08
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:03.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9877.77
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.048
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9830.15
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:05.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.30
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:10.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:04:32.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4821.18
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4969.69
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4223.37
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4021.48
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:27.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11713.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:35.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11660.12
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:38.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.10
p-value of test                       :    0.16


-----------------------------------------------
Total number of bits:  8000010030

Normal statistic for number of bits   :   0.079
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.01
p-value of test                       :    0.30


-----------------------------------------------
Total number of bits:  7999857738

Normal statistic for number of bits   :   -1.12
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:01:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.57
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.41

Tests on the sum of all N observations
Standardized normal statistic         :   -1.07
p-value of test                       :    0.86

Sample variance                       :    1.41
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:18.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Tests on the sum of all N observations
Standardized normal statistic         :   0.081
p-value of test                       :    0.47

Sample variance                       :    0.57
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.44e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.8e-3

Anderson-Darling statistic = A2       :    4.57
p-value of test                       :  4.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.06
p-value of test                       :  1.1e-3

Sample variance                       :    1.05
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:19.72

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:14.46

 All tests were passed




Server wird beendet - Lösche Semaphor 59736076.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
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***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:38.85

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:49.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.95

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.38

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.14

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5401
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4316
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:01:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7117
p-value of test                       :    0.9908


-----------------------------------------------
CPU time used                    :  00:03:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:02:06.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4416
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7340
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:03:53.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:54.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7094
p-value of test                       :    0.9957


-----------------------------------------------
CPU time used                    :  00:04:27.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7277
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:05:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.53


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.52
p-value of test                       :    0.73

Test on the Nm values of W_{n,i}(mNP1):    1.86
p-value of test                       :    0.11

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     583
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.58
p-value of test                       :    0.16

Stat. AD after spacings (mNP2-S)      :    0.95
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:15.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.70
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.93
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:16.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.41
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.83
p-value of test                       :    0.46

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:02:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.84
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.20
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.21
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:58.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.23
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.87
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:12.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.56
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.90
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   69.63
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  203.27
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:27.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1450.78
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:49.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7057.19
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:02:35.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.82
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.74
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:03:11.19

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.48
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:46.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  144.31
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5002.44
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:01:13.02

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:57.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908329
  j =  2                              :            45831
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45749
p-value of test                       :    0.73


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869749
  j =  1                              :        399908506
  j =  2                              :            45741
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    : 5.47e-3
p-value of test                       :    0.9932

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:37.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :  7.3e-3

Anderson-Darling statistic = A2       :    2.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:02:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:00.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.32

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.72


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    2.01
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:19.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:56.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.037
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    3.34
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:18.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:37.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.14e-4
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    : 8.98e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:23.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.69e-4
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    : 7.30e-5
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:24.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.67
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    2.47
p-value of test                       :  6.7e-3

-----------------------------------------------
CPU time used                    :  00:00:23.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.28
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:39.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:39.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.67
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:50.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.63
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.19
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.43
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.49
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:36.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.03
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   15.61
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:46.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.88
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.75
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:04.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.17
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.12
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:25.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:16.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.36
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:06.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.20
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  162.41
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:38.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17469.02
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:53.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   30.14
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.30
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.95
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.95
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.76
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:36.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.37
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.51
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.99
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :    9.32
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.54
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  130.07
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.49
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.86
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  151.02
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.96
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.98
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.12
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.70
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.12
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.88
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:42.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  372.85
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4799.66
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  342.36
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  248.99
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:34.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.25
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  427.17
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4831.47
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.37
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.48
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:34.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.21
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :  -0.015
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:21.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.02
p-value of test                       :    0.86


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:20.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.64
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :    1.48
p-value of test                       :    0.07

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:05.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :   -1.10
p-value of test                       :    0.87

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.26e-3
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.36e-3
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    : 8.41e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.22
p-value of test                       :    0.92

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.32
p-value of test                       :    0.61

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:20.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  176.86
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:02:02.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.075
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  188.78
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:03.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10011.53
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:59.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.39
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:02.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.45
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.93
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.086
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:04:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4906.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:51.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.38
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4991.67
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:53.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.32
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4114.25
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:25.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11969.39
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11580.02
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:30.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.46
p-value of test                       :    0.42


-----------------------------------------------
Total number of bits:  7999929720

Normal statistic for number of bits   :   -0.56
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:05.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.42
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000078538

Normal statistic for number of bits   :    0.62
p-value of test                       :    0.27



-----------------------------------------------
CPU time used                    :  00:01:07.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.44
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.92
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.15
p-value of test                       :    0.02

Sample variance                       :    0.65
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :    1.04
p-value of test                       :    0.15

Sample variance                       :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:12.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.044
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

Tests on the sum of all N observations
Standardized normal statistic         :    1.07
p-value of test                       :    0.14

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:26.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.70

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.95

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:32.29

 All tests were passed




Server wird beendet - Lösche Semaphor 60784652.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:38.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:49.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1414
p-value of test                       :    0.09

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334534
  j =  1                              :        599997172
  j =  2                              :             1414
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.30

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1460
p-value of test                       :  5.3e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334580
  j =  1                              :        599997080
  j =  2                              :             1460
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1429
p-value of test                       :    0.04

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334549
  j =  1                              :        599997142
  j =  2                              :             1429
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.17

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1329
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334449
  j =  1                              :        599997342
  j =  2                              :             1329
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1321
p-value of test                       :    0.88

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334441
  j =  1                              :        599997358
  j =  2                              :             1321
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5429
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:03:58.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4250
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:46.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4341
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:00.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4313
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:02:01.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7363
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:12.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7331
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:12.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:04:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7461
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:04:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.94
p-value of test                       :    0.39

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     886
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.69
p-value of test                       :    0.57

Stat. AD after spacings (mNP2-S)      :    3.98
p-value of test                       :  8.9e-3

-----------------------------------------------
CPU time used                    :  00:01:49.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.90
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.69

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:15.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.38
p-value of test                       :    0.21


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.94
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     291
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.47

Stat. AD after spacings (mNP2-S)      :    0.28
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.44

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.74

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    1.24
p-value of test                       :    0.25

Stat. AD after spacings (mNP2-S)      :    0.32
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:02:48.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.91
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:56.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.57
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.64
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.46
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:12.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.09
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   64.47
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:21.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  251.07
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:24.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  403.20
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:53.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1381.83
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:10.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7048.85
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.45
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:15.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  4.5e-3

Anderson-Darling statistic = A2       :    4.02
p-value of test                       :  8.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   81.54
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:03:13.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.31
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  130.09
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4831.66
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:14.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:03:01.92

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45961
p-value of test                       :    0.35


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869961
  j =  1                              :        399908083
  j =  2                              :            45951
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45783
p-value of test                       :    0.67


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869783
  j =  1                              :        399908437
  j =  2                              :            45777
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.069
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :   0.083
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.55


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:02:21.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.83


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:54.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.05


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:11.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.061
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 7.98e-5
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:23.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.42e-4
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 4.50e-5
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:00:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.09
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :  -0.097
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:40.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.61
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:49.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.73
p-value of test                       :    0.9909

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.98
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.99
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.01
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   22.91
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:45.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   41.52
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:02.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.14
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:02.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.12
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.34
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:25.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.12
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.19
p-value of test                       :    0.9936

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.84
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:39.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17467.52
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:00:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.98
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.56
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.54
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.47
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.80
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:36.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.02
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.13
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.06
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   30.83
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   17.90
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:00:36.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  178.34
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  184.33
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  562.51
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.40
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   78.01
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:00:43.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.15
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  176.03
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  555.89
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.07
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   85.43
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.13
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.69
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.73
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  386.24
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  177.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:35.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.57
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.47
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5109.31
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  391.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  171.10
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.78
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.20
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:20.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.38
p-value of test                       :    0.83


-----------------------------------------------
Normal statistic for number of jumps  :   -0.13
p-value of test                       :    0.55



-----------------------------------------------
CPU time used                    :  00:02:21.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    0.96
p-value of test                       :    0.17

Sample variance                       :    0.44
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:08.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.47
p-value of test                       :  7.2e-3

Anderson-Darling statistic = A2       :    5.44
p-value of test                       :  1.9e-3

Tests on the sum of all N observations
Standardized normal statistic         :    3.17
p-value of test                       :  7.7e-4    *****

Sample variance                       :    1.08
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.06e-3
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:44.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.57e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.95e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:43.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.21
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.95
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:21.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.58
p-value of test                       :    0.05

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  230.67
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:02.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.78
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  241.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:02:03.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10208.11
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:58.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10096.30
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.38
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:00.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:01.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.72
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:06.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4871.60
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:51.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4882.02
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:52.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4107.12
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4119.19
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:24.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11993.79
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.70
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:30.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   81.47
p-value of test                       :  9.2e-3


-----------------------------------------------
Total number of bits:  7999905435

Normal statistic for number of bits   :   -0.75
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:05.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   37.13
p-value of test                       :    0.96


-----------------------------------------------
Total number of bits:  8000029335

Normal statistic for number of bits   :    0.23
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:01:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.51
p-value of test                       :  2.8e-3

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.81
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -1.96
p-value of test                       :    0.97

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:23.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.16
p-value of test                       :    0.56

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:11.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.10

Sample variance                       :    0.58
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:12.09

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:02.37
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 83  LempelZiv, r = 15               7.7e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 61833228.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:00:38.88

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:49.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1381
p-value of test                       :    0.33

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334501
  j =  1                              :        599997238
  j =  2                              :             1381
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:34.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:57.67

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1341
p-value of test                       :    0.73

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334461
  j =  1                              :        599997318
  j =  2                              :             1341
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.45

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1408
p-value of test                       :    0.12

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334528
  j =  1                              :        599997184
  j =  2                              :             1408
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1385
p-value of test                       :    0.29

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334505
  j =  1                              :        599997230
  j =  2                              :             1385
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5495
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4276
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:43.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7350
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4446
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:01.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4232
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:02:03.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7411
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:03:14.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:14.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7192
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:04:11.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7202
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:04:14.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.77
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.67
p-value of test                       :    0.14

Test on the Nm values of W_{n,i}(mNP1):    0.30
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     879
p-value of test                       :    0.75

Stat. AD (mNP2)                       :    1.31
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:50.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.22
p-value of test                       :    0.98

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     582
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.95
p-value of test                       :    0.38

Stat. AD after spacings (mNP2-S)      :    1.07
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:15.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.31
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.13
p-value of test                       :    0.9996    *****

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    4.32
p-value of test                       :  6.1e-3

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.71


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.50
p-value of test                       :    0.74

Test on the Nm values of W_{n,i}(mNP1):    0.98
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:02:45.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.31
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   12.34
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.18
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:15.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.97
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.13
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:25.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.14
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.89
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  431.11
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1308.80
p-value of test                       :    0.9929

-----------------------------------------------
CPU time used                    :  00:02:01.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7109.33
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:57.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   34.50
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   70.91
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.78
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  103.48
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:01:42.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4963.66
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:54.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45897
p-value of test                       :    0.47


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869897
  j =  1                              :        399908207
  j =  2                              :            45895
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:49.51

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46013
p-value of test                       :    0.27


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870013
  j =  1                              :        399907978
  j =  2                              :            46005
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.026
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.026
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:30.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.46


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:15.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:01:45.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:59.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:51.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:14.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.97
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:32.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.25e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.07e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.18
p-value of test                       :    0.9947

-----------------------------------------------
CPU time used                    :  00:00:22.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.83e-5
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 1.44e-4
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.57
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:21.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.59
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:21.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.71
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.41
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:39.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   79.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:52.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.74
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:51.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   40.37
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:49.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.57
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:50.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.47
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:00:48.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.19
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:32.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.86
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   42.58
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:56.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.30
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:17.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.71
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:17.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.58
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:09.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:00.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.31
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:36.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17431.32
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:00:47.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.59
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   52.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.96
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.05
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.50
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:33.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.88
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.79
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.74
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.17
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:34.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  123.64
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  122.94
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  513.92
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.38
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.88
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:39.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  126.18
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.18
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  570.05
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.63
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.03
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:38.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.85
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.42
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4832.57
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  379.22
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.31
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:31.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.98
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  411.64
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4946.66
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  346.73
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  211.03
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:31.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.90
p-value of test                       :    0.31


-----------------------------------------------
Normal statistic for number of jumps  :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:02:08.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.52
p-value of test                       :    0.40


-----------------------------------------------
Normal statistic for number of jumps  :   -1.33
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:02:08.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :    0.56
p-value of test                       :    0.29

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.52
p-value of test                       :    0.94

Sample variance                       :    1.84
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:03.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.72e-3
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    : 6.06e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.54e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:38.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    9.17
p-value of test                       :    0.33

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.54
p-value of test                       :    0.70

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  211.29
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:51.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  181.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9752.48
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9954.86
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:57.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.82
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.90
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.49
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:03:45.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4768.38
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:45.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.93
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4698.77
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:48.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4139.08
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:17.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4193.34
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:19.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11579.25
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11656.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:27.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   47.49
p-value of test                       :    0.72


-----------------------------------------------
Total number of bits:  8000067936

Normal statistic for number of bits   :    0.54
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:00:58.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   50.32
p-value of test                       :    0.62


-----------------------------------------------
Total number of bits:  8000228577

Normal statistic for number of bits   :    1.81
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:59.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.96
p-value of test                       :    0.83

Sample variance                       :    1.76
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:14.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:03.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.49
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:16.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.93
p-value of test                       :    0.82

Sample variance                       :    0.85
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:59.03

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:01:53.25
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP, t = 9           0.9996 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 62881804.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:48.34

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:01.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1417
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334537
  j =  1                              :        599997166
  j =  2                              :             1417
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1395
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334515
  j =  1                              :        599997210
  j =  2                              :             1395
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1416
p-value of test                       :    0.08

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334536
  j =  1                              :        599997168
  j =  2                              :             1416
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:41.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1339
p-value of test                       :    0.75

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334459
  j =  1                              :        599997322
  j =  2                              :             1339
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:19.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:48.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1338
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334458
  j =  1                              :        599997324
  j =  2                              :             1338
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1311
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334431
  j =  1                              :        599997378
  j =  2                              :             1311
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5421
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:03:44.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4269
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:01:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7209
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:36.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:01:54.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4407
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:56.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7570
p-value of test                       :  1.7e-3


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7291
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:03:57.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.81
p-value of test                       :    0.47


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.45
p-value of test                       :    0.80

Test on the Nm values of W_{n,i}(mNP1):    0.57
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     921
p-value of test                       :    0.25

Stat. AD (mNP2)                       :    0.39
p-value of test                       :    0.86

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:52.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.57
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.60
p-value of test                       :    0.64

Test on the Nm values of W_{n,i}(mNP1):    0.64
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     577
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    2.38
p-value of test                       :    0.06

Stat. AD after spacings (mNP2-S)      :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.18
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.28
p-value of test                       :    0.24

Test on the Nm values of W_{n,i}(mNP1):    4.20
p-value of test                       :  7.0e-3

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     348
p-value of test                       :  3.6e-3

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:02:10.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.41
p-value of test                       :    0.83


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.33
p-value of test                       :    0.91

Test on the Nm values of W_{n,i}(mNP1):    0.55
p-value of test                       :    0.70

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     146
p-value of test                       :    0.61

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    0.39
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:02:35.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.41
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:56.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.23
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.66
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:00:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.21
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.43
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:08.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:23.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.65
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.63
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.00
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  379.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:47.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1481.61
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7204.12
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   22.84
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:14.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   66.45
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:03:09.60

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.24
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:44.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   95.62
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:01:39.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5085.93
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:01:16.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:17.10

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45515
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869515
  j =  1                              :        399908975
  j =  2                              :            45505
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:09.59

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46071
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870071
  j =  1                              :        399907861
  j =  2                              :            46065
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:18.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.14


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.63


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:02:17.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:44.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.43

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.61


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.03
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.32

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:53.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:16.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:34.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.66e-4
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    : 1.14e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:22.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 7.75e-5
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:22.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.18
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:22.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.97
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.61
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:44.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.87
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:46.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   74.78
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:51.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.26
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.14
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   30.14
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:52.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.01
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:56.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.64
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:48.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.62
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.17
p-value of test                       :    0.9960

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.06
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.74
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:32.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    9.64
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.63
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:19.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.15
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:39.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17490.53
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:00:55.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   35.44
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.75
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.63
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.83
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.99
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:40.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.34
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.93
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   33.06
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   31.34
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.88
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.44
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  156.93
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  475.93
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  137.27
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.66
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.59
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  520.25
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  134.54
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.45
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:49.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  393.22
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  358.58
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5005.52
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  388.45
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.38
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:39.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  350.58
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  368.88
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5033.23
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.73
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.02
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:39.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.24
p-value of test                       :    0.84


-----------------------------------------------
Normal statistic for number of jumps  :   -0.21
p-value of test                       :    0.58



-----------------------------------------------
CPU time used                    :  00:02:16.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.99
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.63
p-value of test                       :    0.73



-----------------------------------------------
CPU time used                    :  00:02:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -1.00
p-value of test                       :    0.84

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.16
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :   -1.90
p-value of test                       :    0.97

Sample variance                       :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:14.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    : 7.01e-3
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.14
p-value of test                       :    0.74

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.20
p-value of test                       :    0.19

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:24.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.52
p-value of test                       :  2.6e-3

Anderson-Darling statistic = A2       :    2.99
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  239.10
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:02:11.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  175.87
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:02:11.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10236.59
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:59.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    2.15
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10254.81
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.37
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:10.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.98
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:06.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.13
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:04:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.42
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:51.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4773.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:53.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.41
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4087.15
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:25.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11856.52
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:30.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12127.65
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.51
p-value of test                       :    0.09


-----------------------------------------------
Total number of bits:  8000109621

Normal statistic for number of bits   :    0.87
p-value of test                       :    0.19



-----------------------------------------------
CPU time used                    :  00:01:06.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   71.04
p-value of test                       :    0.06


-----------------------------------------------
Total number of bits:  7999895151

Normal statistic for number of bits   :   -0.83
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.96
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.98
p-value of test                       :    0.84

Sample variance                       :    1.24
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:27.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.69

Sample variance                       :    1.25
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:17.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.93
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:30.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:18.98

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:20:53.67

 All tests were passed




Server wird beendet - Lösche Semaphor 42369037.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:00:42.39

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:49.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:13.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1372
p-value of test                       :    0.42

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334492
  j =  1                              :        599997256
  j =  2                              :             1372
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:50.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1384
p-value of test                       :    0.30

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334504
  j =  1                              :        599997232
  j =  2                              :             1384
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:21.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1448
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334568
  j =  1                              :        599997104
  j =  2                              :             1448
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:31.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:26.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:35.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5396
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:03:44.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4448
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7468
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4369
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:01:53.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7257
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:03:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7472
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:03:02.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:57.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:01.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.99
p-value of test                       :    0.36


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    0.26
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     878
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.76
p-value of test                       :    0.51

Stat. AD after spacings (mNP2-S)      :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:49.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.16
p-value of test                       :    0.9974

Test on the Nm values of W_{n,i}(mNP1):    0.46
p-value of test                       :    0.79

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     578
p-value of test                       :    0.81

Stat. AD (mNP2)                       :    1.62
p-value of test                       :    0.15

Stat. AD after spacings (mNP2-S)      :    0.57
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.80
p-value of test                       :    0.48


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.75
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     290
p-value of test                       :    0.71

Stat. AD (mNP2)                       :    2.92
p-value of test                       :    0.03

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:13.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.83

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.80
p-value of test                       :    0.48

Stat. AD after spacings (mNP2-S)      :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   13.65
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.08
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   19.31
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:59.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.53
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:10.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   41.16
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:11.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.02
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   36.01
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:23.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.36
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  194.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  421.46
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1503.66
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:02:05.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7132.06
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   30.50
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:17.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.057
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.21
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.75
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  146.42
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:37.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4889.81
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:01:18.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:01.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46238
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870238
  j =  1                              :        399907526
  j =  2                              :            46234
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.71

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46073
p-value of test                       :    0.18


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870073
  j =  1                              :        399907857
  j =  2                              :            46067
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:11.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.81


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:32.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:21.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:48.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.70
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:54.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:16.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.059
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:35.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.75e-4
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 7.11e-5
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.80e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.57
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:22.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.33
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   0.014
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:38.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.22
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:39.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.78
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:51.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   94.81
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.44
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   26.67
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:56.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.19
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:56.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   22.07
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.30
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:06.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   52.29
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.73
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:31.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.93
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:29.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.32
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:17.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.05
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  127.69
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:40.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17473.21
p-value of test                       :    0.41



-----------------------------------------------
CPU time used                    :  00:00:56.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.62
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.89
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   12.49
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.71
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.87
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   27.93
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.85
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.91
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:40.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.32
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.31
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  534.49
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  133.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   63.35
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:48.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  148.63
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  135.10
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.83
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.89
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   76.13
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:46.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.41
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.91
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5068.11
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  351.00
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.74
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.12
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5101.31
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.65
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.50
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.29
p-value of test                       :    0.23


-----------------------------------------------
Normal statistic for number of jumps  :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:02:17.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.66
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -1.07
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:15.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.72
p-value of test                       :    0.76

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:03.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    1.03
p-value of test                       :    0.15

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.79e-3
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:47.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.11e-3
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:47.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.54
p-value of test                       :    0.90

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:28.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.41
p-value of test                       :    0.60

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.89
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:12.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.14
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:09.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10035.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:59.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10127.06
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.026
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:10.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.57
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:06.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.20
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:04:22.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4834.71
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:53.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.75
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.61
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.58
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11907.65
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:31.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11632.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:31.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.66
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  7999920528

Normal statistic for number of bits   :   -0.63
p-value of test                       :    0.74



-----------------------------------------------
CPU time used                    :  00:01:09.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   56.22
p-value of test                       :    0.39


-----------------------------------------------
Total number of bits:  7999957923

Normal statistic for number of bits   :   -0.33
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:10.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    1.06
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:26.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.61
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:17.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.25
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -0.66
p-value of test                       :    0.75

Sample variance                       :    1.77
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:29.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.54
p-value of test                       :    0.30

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:12.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:14:05.56

 All tests were passed




Server wird beendet - Lösche Semaphor 43220999.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:00:41.54

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:53.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:40.06

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:03.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:26.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:56.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:34.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1332
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334452
  j =  1                              :        599997336
  j =  2                              :             1332
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:00.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1312
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334432
  j =  1                              :        599997376
  j =  2                              :             1312
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:14.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:03.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1344
p-value of test                       :    0.70

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334464
  j =  1                              :        599997312
  j =  2                              :             1344
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:16.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:48.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4379
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7453
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:50.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4285
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:01:59.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4322
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:11.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:29.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7373
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:03:29.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:04:05.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:47.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.58
p-value of test                       :    0.66

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     890
p-value of test                       :    0.62

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:47.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.98
p-value of test                       :    0.37


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.92
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    2.43
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     572
p-value of test                       :    0.87

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:13.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.37
p-value of test                       :    0.88

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.66
p-value of test                       :    0.59

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:02:11.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.74
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.89
p-value of test                       :    0.42

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     138
p-value of test                       :    0.83

Stat. AD (mNP2)                       :    0.30
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:39.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.22
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:54.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.92
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:58.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.58
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.15
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:12.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.19
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.28
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.38
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  275.83
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.30
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:42.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1451.26
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:02:06.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7211.32
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   41.79
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:16.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.40
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:03:08.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.73
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  100.92
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:01:36.82

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5040.08
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:14.01

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:04.85

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45756
p-value of test                       :    0.72


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869756
  j =  1                              :        399908491
  j =  2                              :            45750
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45869
p-value of test                       :    0.52


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869869
  j =  1                              :        399908265
  j =  2                              :            45863
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.74


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:02:39.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:02:28.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.41
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.77


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.30


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.72
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:02:10.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:18.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:36.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.40e-4
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    : 2.69e-4
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.95e-4
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.55
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:22.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.36
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:39.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.91
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:39.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.60
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:57.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.63
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   63.89
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:55.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.34
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.05
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   49.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:55.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   17.20
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.14
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:05.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.80
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.07
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:29.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.98
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:28.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.82
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:16.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.48
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  125.18
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:39.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17502.93
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:00:55.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   33.46
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   20.81
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.05
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.44
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:39.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   25.43
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.86
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.20
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.20
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  194.30
p-value of test                       :  4.6e-3


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.30
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  501.52
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.66
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   77.86
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:00:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  183.34
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.23
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  553.59
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.20
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.44
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.47
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  356.29
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4914.77
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.66
p-value of test                       :    0.55


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  174.04
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:00:48.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.52
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.46
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5067.42
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  377.03
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.39
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:51.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   18.49
p-value of test                       :    0.10


-----------------------------------------------
Normal statistic for number of jumps  :   -1.11
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:20.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.36
p-value of test                       :    0.90


-----------------------------------------------
Normal statistic for number of jumps  :    0.44
p-value of test                       :    0.33



-----------------------------------------------
CPU time used                    :  00:02:20.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.52
p-value of test                       :    0.06

Sample variance                       :    1.12
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.92
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:07.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.69e-3
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    : 5.11e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:46.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.34e-3
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.17
p-value of test                       :    0.84

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:27.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.41
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  194.69
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.89e-3
p-value of test                       :    0.9927

Kolmogorov-Smirnov- statistic = D-    :    0.51
p-value of test                       :  3.0e-3

Anderson-Darling statistic = A2       :    4.56
p-value of test                       :  4.9e-3

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  260.82
p-value of test                       :  2.5e-3

-----------------------------------------------
CPU time used                    :  00:02:08.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9946.79
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:00.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    1.69
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9787.95
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:05.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.41
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:09.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.79
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.81
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:04:22.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4912.01
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:52.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4818.42
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4214.74
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4200.22
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:25.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11798.09
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11861.59
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:30.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   63.67
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  7999907079

Normal statistic for number of bits   :   -0.73
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:12.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.39
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999934100

Normal statistic for number of bits   :   -0.52
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.91
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:25.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -1.26
p-value of test                       :    0.90

Sample variance                       :    1.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:16.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.95
p-value of test                       :    0.17

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:27.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.49
p-value of test                       :  5.3e-3

Anderson-Darling statistic = A2       :    2.33
p-value of test                       :    0.06

Tests on the sum of all N observations
Standardized normal statistic         :    1.60
p-value of test                       :    0.05

Sample variance                       :    0.31
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:16:23.07

 All tests were passed




Server wird beendet - Lösche Semaphor 44498951.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:41.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:51.34

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1439
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334559
  j =  1                              :        599997122
  j =  2                              :             1439
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1435
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334555
  j =  1                              :        599997130
  j =  2                              :             1435
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:24.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1342
p-value of test                       :    0.72

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334462
  j =  1                              :        599997316
  j =  2                              :             1342
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1350
p-value of test                       :    0.64

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334470
  j =  1                              :        599997300
  j =  2                              :             1350
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.43

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1421
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334541
  j =  1                              :        599997158
  j =  2                              :             1421
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:01.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5379
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:03:48.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4310
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:01:38.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7313
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:35.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4334
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:01:53.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4374
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:55.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7248
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:02.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7311
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:03.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7379
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:03:58.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.53
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.54
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.86
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     923
p-value of test                       :    0.23

Stat. AD (mNP2)                       :    0.55
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    1.04
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:47.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.56
p-value of test                       :    0.68


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.77
p-value of test                       :    0.50

Test on the Nm values of W_{n,i}(mNP1):    2.47
p-value of test                       :    0.05

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     562
p-value of test                       :    0.94

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    1.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.11
p-value of test                       :    0.30


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.19
p-value of test                       :    0.27

Test on the Nm values of W_{n,i}(mNP1):    0.85
p-value of test                       :    0.44

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     321
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    3.22
p-value of test                       :    0.02

Stat. AD after spacings (mNP2-S)      :    0.66
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:02:10.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     171
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:37.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.87
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:55.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.28
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.02
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:58.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.54
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:07.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:16.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   76.97
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:29.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.50
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:29.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:30.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.59
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  465.96
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:49.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1458.34
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:02:09.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6891.85
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:50.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   28.59
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:15.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   55.13
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:03:29.94

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.26
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:00:45.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  115.83
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:36.72

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.15
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:13.46

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:03:02.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45633
p-value of test                       :    0.87


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869633
  j =  1                              :        399908736
  j =  2                              :            45629
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45804
p-value of test                       :    0.64


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869804
  j =  1                              :        399908396
  j =  2                              :            45796
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.43


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.031
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59


-----------------------------------------------
CPU time used                    :  00:02:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.96


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:20.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.52


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:01:49.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.18


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:06.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:56.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:18.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.32

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:36.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.53e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 2.06e-4
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 6.07e-5
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:23.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.15
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:41.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:41.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   42.77
p-value of test                       :    0.9908

-----------------------------------------------
CPU time used                    :  00:00:51.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   70.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   58.45
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:55.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.44
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:51.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.04
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.58
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.49
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:46.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.016
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.37
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   60.18
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:04.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.038
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   30.38
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    5.94
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:27.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.73
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:27.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:17.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:07.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.100
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  111.56
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:39.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17175.86
p-value of test                       :    0.91



-----------------------------------------------
CPU time used                    :  00:00:54.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.04
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.56
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   24.58
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.99
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.07
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:39.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.16
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.18
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.39
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   19.58
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:00:39.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  137.84
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.01
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  519.67
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  154.79
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.73
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:46.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  146.44
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.53
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.68
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.40
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   69.71
p-value of test                       :    0.62


-----------------------------------------------
CPU time used                    :  00:00:45.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  315.17
p-value of test                       :    0.9957


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.23
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4955.69
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  362.95
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  219.54
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:36.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.52
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  467.21
p-value of test                       :  2.3e-3


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5135.61
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  343.60
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  195.37
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   16.64
p-value of test                       :    0.16


-----------------------------------------------
Normal statistic for number of jumps  :   -0.14
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:19.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   12.98
p-value of test                       :    0.37


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:19.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :  -0.054
p-value of test                       :    0.52

Sample variance                       :    1.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.67e-3
p-value of test                       :    0.9929

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.09
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :    2.47
p-value of test                       :  6.8e-3

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:46.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    : 3.69e-3
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.56
p-value of test                       :    0.89

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:29.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.90
p-value of test                       :    0.55

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  179.59
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:08.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  191.06
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:02:09.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10116.78
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:00.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.10
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10047.51
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.23
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:07.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.21
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:04.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.16
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:04:24.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4874.57
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:54.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4831.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:55.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4100.11
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:23.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4213.63
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11761.52
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11643.95
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.34
p-value of test                       :    0.29


-----------------------------------------------
Total number of bits:  8000148078

Normal statistic for number of bits   :    1.17
p-value of test                       :    0.12



-----------------------------------------------
CPU time used                    :  00:01:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.31
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  7999952268

Normal statistic for number of bits   :   -0.38
p-value of test                       :    0.65



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.87
p-value of test                       :    0.19

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:26.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.40
p-value of test                       :    0.92

Sample variance                       :    0.79
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:15.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    : 2.47e-3
p-value of test                       :    0.9975

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -1.95
p-value of test                       :    0.97

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    0.82
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:15.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:09:16.51

 All tests were passed




Server wird beendet - Lösche Semaphor 45350919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:41.63

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:00:51.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1345
p-value of test                       :    0.69

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334465
  j =  1                              :        599997310
  j =  2                              :             1345
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.02

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1412
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334532
  j =  1                              :        599997176
  j =  2                              :             1412
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:23.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:51.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1357
p-value of test                       :    0.57

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334477
  j =  1                              :        599997286
  j =  2                              :             1357
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:29.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5539
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:03:52.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4306
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:01:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7410
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:37.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4396
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:01:54.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4387
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:01:56.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7203
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:03:03.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7344
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7491
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:55.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7286
p-value of test                       :    0.64


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.18
p-value of test                       :    0.27


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.73
p-value of test                       :    0.13

Test on the Nm values of W_{n,i}(mNP1):    1.21
p-value of test                       :    0.26

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     918
p-value of test                       :    0.28

Stat. AD (mNP2)                       :    1.92
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:49.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.88
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.36
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.51

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     580
p-value of test                       :    0.79

Stat. AD (mNP2)                       :    1.90
p-value of test                       :    0.10

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:14.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.66


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.84
p-value of test                       :    0.45

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     287
p-value of test                       :    0.76

Stat. AD (mNP2)                       :    0.37
p-value of test                       :    0.88

Stat. AD after spacings (mNP2-S)      :    0.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:02:15.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.97
p-value of test                       :    0.10

Test on the Nm values of W_{n,i}(mNP1):    0.62
p-value of test                       :    0.63

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.93
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:45.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.19
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.94
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:03.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.75
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:58.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   10.64
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:06.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.99
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:09.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.24
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:22.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.00
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.00
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:22.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  283.06
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:24.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  408.82
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:49.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1397.29
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7136.27
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:50.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.42
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   38.02
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:15.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   60.94
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:03:08.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.25
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:46.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  157.07
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:01:36.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4825.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:03:20.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45981
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869981
  j =  1                              :        399908038
  j =  2                              :            45981
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.82

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45878
p-value of test                       :    0.50


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869878
  j =  1                              :        399908246
  j =  2                              :            45874
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:30.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.03


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.019
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    2.07
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:20.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.071
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.35


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:01:48.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:02:06.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:56.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:18.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:36.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.58e-4
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:23.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.15e-4
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    : 9.00e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :  -0.017
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:23.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.90
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:45.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.54
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:00:55.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.09
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   47.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:51.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.99
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   25.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:55.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.63
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:46.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.01
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:03.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.01
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.71
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:28.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.79
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :   0.075
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:17.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.03
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  137.63
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17344.51
p-value of test                       :    0.68



-----------------------------------------------
CPU time used                    :  00:00:53.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   44.05
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.08
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.58
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   20.28
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.10
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.10
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.23
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.78
p-value of test                       :    0.42


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.30
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.74
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:38.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.68
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.33
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  479.02
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  113.52
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   71.77
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:45.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.27
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.45
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  459.21
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  100.02
p-value of test                       :    0.9911


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   88.21
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:45.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.53
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  364.47
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4905.96
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.21
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.22
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:36.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.25
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  429.60
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4906.16
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  401.06
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.85
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   14.42
p-value of test                       :    0.27


-----------------------------------------------
Normal statistic for number of jumps  :   -0.93
p-value of test                       :    0.82



-----------------------------------------------
CPU time used                    :  00:02:22.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.84
p-value of test                       :    0.72


-----------------------------------------------
Normal statistic for number of jumps  :   -1.14
p-value of test                       :    0.87



-----------------------------------------------
CPU time used                    :  00:02:20.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.55
p-value of test                       :    0.29

Sample variance                       :    0.59
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:10.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Tests on the sum of all N observations
Standardized normal statistic         :    1.49
p-value of test                       :    0.07

Sample variance                       :    1.38
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:08.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.99e-3
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:45.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.023
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:44.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.12
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:26.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.31
p-value of test                       :    0.14

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.28
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.50
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  169.04
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.81e-3
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    4.32
p-value of test                       :  6.4e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10423.60
p-value of test                       :  1.5e-3

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9833.55
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.04
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:11.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :  -0.049
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:05.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.18
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:04:22.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4806.42
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:54.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4854.06
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:54.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4170.73
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4101.95
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12144.20
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:32.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11999.33
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:32.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.01
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  8000179722

Normal statistic for number of bits   :    1.42
p-value of test                       :    0.08



-----------------------------------------------
CPU time used                    :  00:01:05.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.12
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  8000121414

Normal statistic for number of bits   :    0.96
p-value of test                       :    0.17



-----------------------------------------------
CPU time used                    :  00:01:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :  -0.087
p-value of test                       :    0.53

Sample variance                       :    0.40
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.21
p-value of test                       :    0.11

Sample variance                       :    2.23
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :   -0.33
p-value of test                       :    0.63

Sample variance                       :    1.42
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:27.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.095
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :    0.98
p-value of test                       :    0.16

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.71

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:24.31

 All tests were passed




Server wird beendet - Lösche Semaphor 46366727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:00:39.74

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:51.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1297
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334417
  j =  1                              :        599997406
  j =  2                              :             1297
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1303
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334423
  j =  1                              :        599997394
  j =  2                              :             1303
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.08

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1411
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334531
  j =  1                              :        599997178
  j =  2                              :             1411
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:47.01

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:22.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1316
p-value of test                       :    0.90

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334436
  j =  1                              :        599997368
  j =  2                              :             1316
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:52.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5427
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:04:00.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:42.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7229
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:53.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4342
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4151
p-value of test                       :    0.9977


-----------------------------------------------
CPU time used                    :  00:02:12.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7223
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:31.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7321
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:30.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7169
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:04:08.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:04:50.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.69
p-value of test                       :    0.56


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.16
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.28
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     933
p-value of test                       :    0.14

Stat. AD (mNP2)                       :    0.47
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    1.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:46.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.97
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.27
p-value of test                       :    0.24

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     573
p-value of test                       :    0.86

Stat. AD (mNP2)                       :    0.57
p-value of test                       :    0.67

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.35
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.61
p-value of test                       :    0.63

Test on the Nm values of W_{n,i}(mNP1):    1.60
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     340
p-value of test                       :    0.01

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.78

Stat. AD after spacings (mNP2-S)      :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:10.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.45
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.62
p-value of test                       :    0.62

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     144
p-value of test                       :    0.67

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.45

Stat. AD after spacings (mNP2-S)      :    0.21
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:39.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.01
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:54.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.75
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:05.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   24.19
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:57.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.04
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:06.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.86
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:11.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.90
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:21.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.22
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.31
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:22.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  439.84
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:47.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1438.50
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:06.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7075.53
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:50.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.46
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   27.82
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.53
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:03:09.13

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.72
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:00:44.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  114.13
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:36.28

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5074.69
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:12.84

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:03.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45668
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869668
  j =  1                              :        399908671
  j =  2                              :            45654
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45661
p-value of test                       :    0.85


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869661
  j =  1                              :        399908686
  j =  2                              :            45645
  j =  3                              :                8
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:39.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.059
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:02:36.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.59


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:02:02.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.043
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:20.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 9.86e-3
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:56.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:18.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:36.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.98e-4
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    : 2.32e-4
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    2.05
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.53e-4
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 1.15e-4
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.47
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:23.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.28
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.51
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:43.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.08
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   53.78
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:57.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   82.79
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:14.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.54
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:14.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.48
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:56.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.25
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:14.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.57
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:13.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   31.67
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:46.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   55.92
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:06.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   48.17
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:06.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.48
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.30
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:07.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :   0.082
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  117.28
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:39.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.95
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17133.95
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:00:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.33
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.75
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.09
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.27
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.14
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:38.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.68
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.34
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.06
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.98
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.87
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:38.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.11
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  132.52
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  525.49
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  110.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.35
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:45.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.40
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.89
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  508.02
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  152.76
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  103.86
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  402.94
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.08
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5095.45
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  392.32
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  189.86
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:00:36.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  389.50
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.50
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5028.85
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  404.81
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.73
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:36.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.93
p-value of test                       :    0.45


-----------------------------------------------
Normal statistic for number of jumps  :    1.33
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.56
p-value of test                       :    0.48


-----------------------------------------------
Normal statistic for number of jumps  :   -1.09
p-value of test                       :    0.86



-----------------------------------------------
CPU time used                    :  00:02:20.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.79
p-value of test                       :    0.12

Tests on the sum of all N observations
Standardized normal statistic         :   -0.86
p-value of test                       :    0.81

Sample variance                       :    1.57
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :  -0.011
p-value of test                       :    0.50

Sample variance                       :    1.47
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.40e-3
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    : 8.28e-3
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:46.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 4.66e-3
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.04
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:27.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   15.36
p-value of test                       :    0.05

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.063
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  187.58
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:06.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  217.14
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:02:07.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10082.83
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:00.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10041.54
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.61
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:09.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:04:21.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.36
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4701.92
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:54.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4836.72
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4204.14
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3956.27
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11712.17
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:33.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11832.73
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:32.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   55.07
p-value of test                       :    0.43


-----------------------------------------------
Total number of bits:  8000044533

Normal statistic for number of bits   :    0.35
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:07.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   73.68
p-value of test                       :    0.04


-----------------------------------------------
Total number of bits:  7999913370

Normal statistic for number of bits   :   -0.68
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:01:08.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  4.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    4.33
p-value of test                       :  6.3e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.36
p-value of test                       :    0.9908

Sample variance                       :    0.28
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    1.03
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.28

Sample variance                       :    0.94
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.91
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :   -0.61
p-value of test                       :    0.73

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:16.89

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:12:36.81

 All tests were passed




Server wird beendet - Lösche Semaphor 47284231.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:39.36

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:00:50.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.63

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.18

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1367
p-value of test                       :    0.47

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334487
  j =  1                              :        599997266
  j =  2                              :             1367
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.89

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5385
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:03:59.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4352
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:42.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7327
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:02:41.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4402
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4147
p-value of test                       :    0.9981


-----------------------------------------------
CPU time used                    :  00:01:57.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7196
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:03:04.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7330
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:03:56.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7346
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:03:58.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.14
p-value of test                       :    0.29

Test on the Nm values of W_{n,i}(mNP1):    1.82
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     965
p-value of test                       :    0.02

Stat. AD (mNP2)                       :    0.25
p-value of test                       :    0.97

Stat. AD after spacings (mNP2-S)      :    0.83
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.58
p-value of test                       :    0.67


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.36

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     563
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.83
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:13.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.18
p-value of test                       :    0.9951


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.92
p-value of test                       :    0.40

Test on the Nm values of W_{n,i}(mNP1):    0.48
p-value of test                       :    0.77

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.46
p-value of test                       :    0.79

Stat. AD after spacings (mNP2-S)      :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:02:11.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.13
p-value of test                       :    0.08


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.42
p-value of test                       :    0.82

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     142
p-value of test                       :    0.73

Stat. AD (mNP2)                       :    0.44
p-value of test                       :    0.81

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:40.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.12
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:55.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   18.70
p-value of test                       :  9.2e-3

-----------------------------------------------
CPU time used                    :  00:01:04.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.54
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:00:57.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.36
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:06.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.36
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:11.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   38.12
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:21.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.67
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:21.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.16
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:22.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.86
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  454.39
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1491.91
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:05.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6873.37
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:51.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   17.40
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:16.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   74.95
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:03:09.59

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    8.61
p-value of test                       :    0.13


-----------------------------------------------
CPU time used                    :  00:00:46.18

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  110.63
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:01:36.85

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4973.45
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:01:12.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:07.56

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46277
p-value of test                       :    0.03


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870277
  j =  1                              :        399907450
  j =  2                              :            46269
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.60

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46066
p-value of test                       :    0.19


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870066
  j =  1                              :        399907874
  j =  2                              :            46054
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.027
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.59
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 3.99e+6
p-value of test                       :    0.99


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    1.86
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:02:29.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.38


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.023
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:01:47.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.45


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:02:05.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:55.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.065
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:17.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:35.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.26e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.35e-5
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    : 1.36e-4
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.64
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:23.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.68
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:41.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:42.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.99
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.47
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:00:56.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   78.20
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:55.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   52.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:49.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.80
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:55.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.93
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:00:55.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   20.78
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:45.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.30
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   50.37
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:03.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   57.28
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:04.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.84
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.98
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:26.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.61
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.34
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    2.39
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  152.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:39.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17582.92
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:00:53.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.03
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.19
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.66
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.01
p-value of test                       :    0.46


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.95
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:37.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   38.60
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   23.21
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   17.07
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   15.22
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.74
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:00:37.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.57
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  531.19
p-value of test                       :    0.16


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.21
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.94
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:44.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.64
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.24
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.59
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  139.61
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   54.34
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.30
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  422.69
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5050.34
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  399.16
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  209.49
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:00:35.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.98
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.91
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4936.89
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  406.20
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  205.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:34.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.22
p-value of test                       :    0.51


-----------------------------------------------
Normal statistic for number of jumps  :   -1.02
p-value of test                       :    0.85



-----------------------------------------------
CPU time used                    :  00:02:21.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.83
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :    1.50
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:02:21.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Tests on the sum of all N observations
Standardized normal statistic         :   -0.35
p-value of test                       :    0.64

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:04.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.50

Tests on the sum of all N observations
Standardized normal statistic         :    0.36
p-value of test                       :    0.36

Sample variance                       :    1.32
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.88e-3
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :   0.017
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:00:45.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    : 5.28e-3
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.88
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   10.75
p-value of test                       :    0.22

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.00
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:07.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  9.1e-3

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.34
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.17
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:06.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9964.59
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10009.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:02.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.14
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:09.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.89
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:04:20.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5029.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4815.07
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:55.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4131.91
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4176.75
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:26.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12081.71
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:32.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12030.70
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:32.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   49.40
p-value of test                       :    0.65


-----------------------------------------------
Total number of bits:  8000037648

Normal statistic for number of bits   :    0.30
p-value of test                       :    0.38



-----------------------------------------------
CPU time used                    :  00:01:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   41.44
p-value of test                       :    0.89


-----------------------------------------------
Total number of bits:  8000041272

Normal statistic for number of bits   :    0.33
p-value of test                       :    0.37



-----------------------------------------------
CPU time used                    :  00:01:09.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    : 4.60e-3
p-value of test                       :    0.9952

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.60
p-value of test                       :    0.94

Sample variance                       :    1.22
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:25.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Tests on the sum of all N observations
Standardized normal statistic         :   -0.25
p-value of test                       :    0.60

Sample variance                       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:13.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Tests on the sum of all N observations
Standardized normal statistic         :    0.78
p-value of test                       :    0.22

Sample variance                       :    0.80
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:28.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :    0.83
p-value of test                       :    0.20

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.01

 All tests were passed




Server wird beendet - Lösche Semaphor 48300039.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:00:39.32

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:50.37

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1410
p-value of test                       :    0.11

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334530
  j =  1                              :        599997180
  j =  2                              :             1410
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:12.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:36.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1427
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334547
  j =  1                              :        599997146
  j =  2                              :             1427
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1347
p-value of test                       :    0.67

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334467
  j =  1                              :        599997306
  j =  2                              :             1347
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.96

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1327
p-value of test                       :    0.84

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334447
  j =  1                              :        599997346
  j =  2                              :             1327
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1388
p-value of test                       :    0.26

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334508
  j =  1                              :        599997224
  j =  2                              :             1388
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.04

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1370
p-value of test                       :    0.44

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334490
  j =  1                              :        599997260
  j =  2                              :             1370
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5457
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:02.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4318
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7228
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:44.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4296
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:59.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4230
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:00.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:10.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7336
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7237
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:03:57.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7408
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:03:59.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.85
p-value of test                       :    0.03


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.48

Test on the Nm values of W_{n,i}(mNP1):    0.29
p-value of test                       :    0.94

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     908
p-value of test                       :    0.40

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.35
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.92
p-value of test                       :    0.40


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.52
p-value of test                       :    0.17

Test on the Nm values of W_{n,i}(mNP1):    0.91
p-value of test                       :    0.41

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     610
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.30

Stat. AD after spacings (mNP2-S)      :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.74
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    1.59
p-value of test                       :    0.16

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     308
p-value of test                       :    0.33

Stat. AD (mNP2)                       :    6.62
p-value of test                       :  5.1e-4    *****

Stat. AD after spacings (mNP2-S)      :    1.15
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:02:13.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.47
p-value of test                       :    0.77


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.72
p-value of test                       :    0.53

Test on the Nm values of W_{n,i}(mNP1):    0.93
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     162
p-value of test                       :    0.17

Stat. AD (mNP2)                       :    0.23
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:02:40.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.21
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:00:54.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.75
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:03.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.70
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.70
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.67
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.87
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:20.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.26
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:20.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.28
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:21.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  261.26
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  426.73
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:47.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1389.60
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:02:04.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6955.48
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:49.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.40
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:15.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   49.97
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:03:07.61

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    2.64
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  138.64
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:01:35.89

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5054.56
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:13.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:03:03.42

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45496
p-value of test                       :    0.96


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869496
  j =  1                              :        399909015
  j =  2                              :            45482
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.63

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45662
p-value of test                       :    0.84


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869662
  j =  1                              :        399908678
  j =  2                              :            45658
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.021
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.16


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:30.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.098
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:02:18.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.60


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:48.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.057
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.20


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:02:05.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.046
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:55.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:18.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.65e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 1.54e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.89
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:23.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.56e-4
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.12
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:23.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.83
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.26
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.43
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   73.84
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   51.00
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:49.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.66
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.67
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:55.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   28.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:46.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.076
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.28
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.54
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.10
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:26.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.52
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.47
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    : 5.62e-3
p-value of test                       :    0.9941

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :   98.60
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:39.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17191.84
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:00:52.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   32.92
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.22
p-value of test                       :    0.70


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   23.66
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.98
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   21.25
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:36.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   39.92
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.10
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   31.47
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   19.48
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.35
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:37.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.69
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.87
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  564.45
p-value of test                       :    0.02


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  146.21
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   68.80
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:00:44.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  172.51
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  145.27
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  527.77
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  147.19
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.85
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:00:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  366.72
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.04
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4907.99
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  415.21
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  201.14
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  381.04
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.70
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4980.79
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  373.01
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  184.25
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:36.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.98
p-value of test                       :    0.19


-----------------------------------------------
Normal statistic for number of jumps  :    0.47
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:21.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.34
p-value of test                       :    0.34


-----------------------------------------------
Normal statistic for number of jumps  :   0.075
p-value of test                       :    0.47



-----------------------------------------------
CPU time used                    :  00:02:21.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.26
p-value of test                       :    0.40

Sample variance                       :    1.35
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:04.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

Tests on the sum of all N observations
Standardized normal statistic         :    0.33
p-value of test                       :    0.37

Sample variance                       :    0.70
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.53e-3
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.41
p-value of test                       :    0.97

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:24.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.78
p-value of test                       :    0.88

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.38

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.55
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  186.36
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:05.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10161.31
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9924.94
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:02.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.10
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:09.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.43
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:04:13.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.097
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.76

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4899.03
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:52.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4935.65
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:55.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4283.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4030.39
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12128.13
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:31.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11686.13
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   70.20
p-value of test                       :    0.07


-----------------------------------------------
Total number of bits:  7999807917

Normal statistic for number of bits   :   -1.52
p-value of test                       :    0.94



-----------------------------------------------
CPU time used                    :  00:01:07.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.21
p-value of test                       :    0.47


-----------------------------------------------
Total number of bits:  7999893360

Normal statistic for number of bits   :   -0.84
p-value of test                       :    0.80



-----------------------------------------------
CPU time used                    :  00:01:08.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.55
p-value of test                       :    0.94

Sample variance                       :    0.95
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:25.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :   -1.41
p-value of test                       :    0.92

Sample variance                       :    1.55
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:15.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :  -0.047
p-value of test                       :    0.52

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:28.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.89e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.87
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :    1.87
p-value of test                       :    0.03

Sample variance                       :    0.74
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:39.21
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 24  ClosePairs mNP2, t = 9          5.1e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 49348615.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:00:40.68

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1361
p-value of test                       :    0.53

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334481
  j =  1                              :        599997278
  j =  2                              :             1361
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1484
p-value of test                       :  7.2e-4    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334604
  j =  1                              :        599997032
  j =  2                              :             1484
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.94

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1375
p-value of test                       :    0.39

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334495
  j =  1                              :        599997250
  j =  2                              :             1375
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.16

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1401
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334521
  j =  1                              :        599997198
  j =  2                              :             1401
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5360
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:04:03.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4415
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:01:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7362
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:45.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4315
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:02:02.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:03:14.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:03:12.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7225
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:04:08.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7351
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:04:08.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.09
p-value of test                       :    0.02


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.44
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     944
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    1.50
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    1.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.79
p-value of test                       :    0.12


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.35
p-value of test                       :    0.22

Test on the Nm values of W_{n,i}(mNP1):    1.43
p-value of test                       :    0.19

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     638
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.82
p-value of test                       :    0.46

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:13.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.31
p-value of test                       :    0.06


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.91
p-value of test                       :    0.41

Test on the Nm values of W_{n,i}(mNP1):    1.80
p-value of test                       :    0.12

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     258
p-value of test                       :    0.9928

Stat. AD (mNP2)                       :    1.09
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    2.18
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.94
p-value of test                       :    0.39

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     154
p-value of test                       :    0.38

Stat. AD (mNP2)                       :    0.90
p-value of test                       :    0.41

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:38.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:57.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    1.78
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.23
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:01.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   21.92
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:10.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.87
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:13.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:25.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.56
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  217.84
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:30.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  432.45
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:56.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1369.07
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:08.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7064.59
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:57.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:18.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.70
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:03:21.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.09
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:47.47

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  129.28
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:01:44.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5059.39
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:01:24.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:03:02.53

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46052
p-value of test                       :    0.21


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870052
  j =  1                              :        399907897
  j =  2                              :            46050
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907920
  j =  2                              :            46034
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.078
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.62


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.067
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:32.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :  9.9e-3

Kolmogorov-Smirnov- statistic = D-    :   0.019
p-value of test                       :    0.97

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 2.99e+6
p-value of test                       :    0.9930


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.038
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.12
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:02:21.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.50


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :   0.085
p-value of test                       :    0.71

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:01:52.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.33
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:08.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.42
p-value of test                       :  5.6e-4    *****

Kolmogorov-Smirnov- statistic = D-    :   0.039
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    6.18
p-value of test                       :  8.4e-4    *****

-----------------------------------------------
CPU time used                    :  00:01:19.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    : 1.04e-4
p-value of test                       :    0.9999    *****

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:37.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.27e-4
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 1.08e-4
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    2.32
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.92e-5
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    : 1.09e-4
p-value of test                       :    0.62

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:24.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:24.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.44
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    2.42
p-value of test                       :  7.7e-3

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.59
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:49.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.55
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:51.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   69.51
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:00:58.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.27
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:58.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   55.02
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:00:50.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   43.88
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.53
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:58.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.88
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:51.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.95
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.54

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   37.09
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.26
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:26.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    6.02
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.85
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:16.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:06.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  120.87
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:41.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.099
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17537.51
p-value of test                       :    0.28



-----------------------------------------------
CPU time used                    :  00:00:52.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   37.25
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.06
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.54
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   29.83
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.96
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:36.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.56
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.25
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.49
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.80
p-value of test                       :    0.53


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.16
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:36.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.57
p-value of test                       :    0.40


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  129.77
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  491.12
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  119.86
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.32
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:00:43.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  114.41
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.37
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  554.26
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  112.17
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   53.57
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:43.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  403.76
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.70
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5029.46
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  412.78
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  226.46
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:00:35.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  437.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.19
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5057.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.16
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  224.12
p-value of test                       :    0.12


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.84
p-value of test                       :    0.63


-----------------------------------------------
Normal statistic for number of jumps  :  -0.010
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:23.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.09
p-value of test                       :    0.91


-----------------------------------------------
Normal statistic for number of jumps  :   -0.99
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:02:23.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.38

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    1.40
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:04.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.068
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.28
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.17
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.81e-3
p-value of test                       :    0.45

Kolmogorov-Smirnov- statistic = D-    : 4.06e-3
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:45.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.40e-3
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:44.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.78
p-value of test                       :    0.67

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    3.30
p-value of test                       :    0.91

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  208.15
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:02:05.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.34
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    2.18
p-value of test                       :    0.07

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  163.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10014.66
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:00.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 5.56e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    3.15
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9644.73
p-value of test                       :    0.9944

-----------------------------------------------
CPU time used                    :  00:01:05.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.65
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:10.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:07.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.53
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:04:30.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.33

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4819.10
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:55.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.063
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4930.38
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:58.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4292.80
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:25.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4185.82
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:27.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11588.30
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:35.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11829.77
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.59
p-value of test                       :    0.53


-----------------------------------------------
Total number of bits:  8000085330

Normal statistic for number of bits   :    0.67
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:05.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   76.00
p-value of test                       :    0.03


-----------------------------------------------
Total number of bits:  7999887801

Normal statistic for number of bits   :   -0.89
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:01:08.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.69

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:25.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.30
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -1.47
p-value of test                       :    0.93

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

Tests on the sum of all N observations
Standardized normal statistic         :   -0.11
p-value of test                       :    0.54

Sample variance                       :    1.86
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:26.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    1.71
p-value of test                       :    0.13

Tests on the sum of all N observations
Standardized normal statistic         :   -0.80
p-value of test                       :    0.79

Sample variance                       :    0.18
p-value of test                       :    0.9963

-----------------------------------------------
CPU time used                    :  00:01:18.38

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:52.28
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
  7  CollisionOver, t = 7            7.2e-4
 51  SampleProd, t = 16              8.4e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 50397191.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:40.90

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:50.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1296
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334416
  j =  1                              :        599997408
  j =  2                              :             1296
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.88

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.50

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.58

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1333
p-value of test                       :    0.80

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334453
  j =  1                              :        599997334
  j =  2                              :             1333
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.20

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1378
p-value of test                       :    0.36

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334498
  j =  1                              :        599997244
  j =  2                              :             1378
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1335
p-value of test                       :    0.78

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334455
  j =  1                              :        599997330
  j =  2                              :             1335
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.78

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1383
p-value of test                       :    0.31

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334503
  j =  1                              :        599997234
  j =  2                              :             1383
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.11

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1379
p-value of test                       :    0.35

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334499
  j =  1                              :        599997242
  j =  2                              :             1379
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5528
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:04:00.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:44.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7231
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:02:46.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4257
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4270
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:02:01.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7119
p-value of test                       :    0.9902


-----------------------------------------------
CPU time used                    :  00:03:08.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7370
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:07.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7312
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:03:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7545
p-value of test                       :  4.2e-3


-----------------------------------------------
CPU time used                    :  00:03:59.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.25
p-value of test                       :    0.97


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.59
p-value of test                       :    0.65

Test on the Nm values of W_{n,i}(mNP1):    0.67
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.36
p-value of test                       :    0.89

Stat. AD after spacings (mNP2-S)      :    1.10
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.64
p-value of test                       :    0.15

Test on the Nm values of W_{n,i}(mNP1):    0.38
p-value of test                       :    0.87

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.69

Stat. AD after spacings (mNP2-S)      :    0.24
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:14.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.71
p-value of test                       :    0.55


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.52

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:02:13.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.28
p-value of test                       :    0.95


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.75
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.28
p-value of test                       :    0.95

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     143
p-value of test                       :    0.70

Stat. AD (mNP2)                       :    0.60
p-value of test                       :    0.65

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:02:39.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.74
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:54.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.53
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:03.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   26.42
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:00:57.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.00
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:06.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   43.94
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:12.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.10
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:20.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   47.62
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:21.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.16
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:21.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  259.67
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  484.64
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:48.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1391.09
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:02:05.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7210.37
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   32.88
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   67.88
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:03:09.35

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.72
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.36
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:36.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5120.45
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45547
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869547
  j =  1                              :        399908910
  j =  2                              :            45539
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.84

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46086
p-value of test                       :    0.17


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870086
  j =  1                              :        399907831
  j =  2                              :            46080
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :  8.2e-3

Anderson-Darling statistic = A2       :    2.86
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.33


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:02:30.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.035
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.13


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.047
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.20
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:19.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.88


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:01:46.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.072
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.40


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:05.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    1.14
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:18.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.065
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:36.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.19e-4
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    : 1.63e-4
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:23.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.48e-4
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 1.73e-4
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:23.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.53
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:23.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.25
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:22.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -2.13
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:38.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      : -6.86e-4
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:38.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.01
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:00:50.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.92
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:00:56.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.34
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:56.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.61
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:50.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   17.94
p-value of test                       :    0.9965

-----------------------------------------------
CPU time used                    :  00:00:56.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   31.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:56.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   29.67
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.088
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   43.07
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:03.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.85
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:03.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:26.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.51
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.01
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:16.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    4.39
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.82

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:38.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.84

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17245.98
p-value of test                       :    0.84



-----------------------------------------------
CPU time used                    :  00:00:52.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   49.30
p-value of test                       :    0.07


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.84
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   10.95
p-value of test                       :    0.9932


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   27.32
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    9.46
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.66
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.36
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.14
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   16.36
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   14.59
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:37.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  149.36
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  131.01
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  443.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  162.69
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   89.50
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:00:43.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  153.07
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.37
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  481.45
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.90
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   48.16
p-value of test                       :    0.9914


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  377.79
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  391.59
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5013.01
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  363.67
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.30
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  355.85
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  407.84
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4979.15
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.69
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  191.14
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:00:35.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.33
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :    0.38
p-value of test                       :    0.35



-----------------------------------------------
CPU time used                    :  00:02:22.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.23
p-value of test                       :    0.35


-----------------------------------------------
Normal statistic for number of jumps  :    0.46
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:02:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.90

Tests on the sum of all N observations
Standardized normal statistic         :    0.16
p-value of test                       :    0.44

Sample variance                       :    0.88
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:04.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

Tests on the sum of all N observations
Standardized normal statistic         :    0.46
p-value of test                       :    0.32

Sample variance                       :    0.77
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:06.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 3.36e-3
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.98
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:00:45.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.70e-3
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.76
p-value of test                       :    0.03

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:24.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.49
p-value of test                       :    0.59

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:22.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.17
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.089
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.36
p-value of test                       :    0.06

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  222.99
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:02:05.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10004.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:59.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.40
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    2.14
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9751.85
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:02.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.50
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:08.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:04.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:04:17.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.38
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.31
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4697.68
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:53.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.032
p-value of test                       :    0.96

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5069.86
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:54.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4181.42
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4188.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11778.77
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:01:31.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.46
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.59
p-value of test                       :    0.57


-----------------------------------------------
Total number of bits:  7999959327

Normal statistic for number of bits   :   -0.32
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:01:07.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.03
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000104011

Normal statistic for number of bits   :    0.82
p-value of test                       :    0.21



-----------------------------------------------
CPU time used                    :  00:01:09.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.26
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.06
p-value of test                       :    0.33

Tests on the sum of all N observations
Standardized normal statistic         :   -1.31
p-value of test                       :    0.90

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Tests on the sum of all N observations
Standardized normal statistic         :   -0.32
p-value of test                       :    0.63

Sample variance                       :    0.91
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:17.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :   -0.92
p-value of test                       :    0.82

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:27.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.86

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    1.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:14.56

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:00.50

 All tests were passed




Server wird beendet - Lösche Semaphor 51478535.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:00:39.15

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:00:50.57

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.68

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1382
p-value of test                       :    0.32

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334502
  j =  1                              :        599997236
  j =  2                              :             1382
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1413
p-value of test                       :    0.10

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334533
  j =  1                              :        599997174
  j =  2                              :             1413
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1349
p-value of test                       :    0.65

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334469
  j =  1                              :        599997302
  j =  2                              :             1349
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1324
p-value of test                       :    0.86

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334444
  j =  1                              :        599997352
  j =  2                              :             1324
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.39

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1437
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334557
  j =  1                              :        599997126
  j =  2                              :             1437
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1230
p-value of test                       :    0.9999    *****

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334350
  j =  1                              :        599997540
  j =  2                              :             1230
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5375
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:02.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4211
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:44.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7455
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:02:45.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4363
p-value of test                       :    0.35


-----------------------------------------------
CPU time used                    :  00:02:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4331
p-value of test                       :    0.53


-----------------------------------------------
CPU time used                    :  00:02:01.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7293
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:03:08.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7493
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:03:08.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7401
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:03.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7245
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:04:01.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.91
p-value of test                       :    0.41


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.23
p-value of test                       :    0.98

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.69

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     855
p-value of test                       :    0.93

Stat. AD (mNP2)                       :    0.85
p-value of test                       :    0.44

Stat. AD after spacings (mNP2-S)      :    0.45
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:47.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.88
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.88
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.97
p-value of test                       :    0.10

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     644
p-value of test                       :    0.04

Stat. AD (mNP2)                       :    4.06
p-value of test                       :  8.1e-3

Stat. AD after spacings (mNP2-S)      :    1.77
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:14.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.75
p-value of test                       :    0.52


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.81
p-value of test                       :    0.12

Test on the Nm values of W_{n,i}(mNP1):    0.74
p-value of test                       :    0.52

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     288
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    0.29
p-value of test                       :    0.94

Stat. AD after spacings (mNP2-S)      :    0.82
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:02:14.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.36
p-value of test                       :    0.89


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.80
p-value of test                       :    0.47

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     149
p-value of test                       :    0.51

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.48
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:02:39.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.82
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.24
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.62
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:00:58.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   27.00
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   37.06
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:12.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.27
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:21.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.22
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.38
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  282.27
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:22.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  446.38
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:47.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1446.53
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:05.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6934.49
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:49.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.40
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:15.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.016
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.08
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   45.42
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:03:09.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.89
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:00:45.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.93
p-value of test                       :    0.36


-----------------------------------------------
CPU time used                    :  00:01:36.90

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5101.50
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:13.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:03:17.86

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45795
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869795
  j =  1                              :        399908413
  j =  2                              :            45789
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:55.19

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45916
p-value of test                       :    0.43


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869916
  j =  1                              :        399908174
  j =  2                              :            45904
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.039
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.074
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65


-----------------------------------------------
CPU time used                    :  00:02:32.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 1.42e-3
p-value of test                       :    0.9985

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    2.40
p-value of test                       :    0.06

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.01e+6
p-value of test                       :  9.2e-3


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    : 2.50e-3
p-value of test                       :    0.9973

Anderson-Darling statistic = A2       :    2.00
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:02:25.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52


-----------------------------------------------
CPU time used                    :  00:01:54.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.19


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.035
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:02:11.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:55.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.049
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:17.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    3.01
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:35.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.76e-5
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    : 1.12e-4
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.01e-4
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.13
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:23.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.11
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:41.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.71
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:41.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.99
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:49.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   81.77
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   57.18
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:56.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.88
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:49.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.50
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   27.17
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   19.58
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:45.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    1.59
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   26.50
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:04.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.78

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   40.20
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:04.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.33
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:27.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.49
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:17.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.46
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  139.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:39.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17365.85
p-value of test                       :    0.63



-----------------------------------------------
CPU time used                    :  00:00:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.14
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.65
p-value of test                       :    0.48


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   26.27
p-value of test                       :    0.39


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   13.32
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   22.31
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:00:37.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   36.63
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   29.76
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.30
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   10.65
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  175.84
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  166.68
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  511.65
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  145.42
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   86.06
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:00:44.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  164.63
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  168.27
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  467.77
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  104.96
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:00:43.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.27
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  367.07
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4998.35
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  414.01
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  193.02
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:34.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.30
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  339.75
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5040.10
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  365.05
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  240.82
p-value of test                       :    0.03


-----------------------------------------------
CPU time used                    :  00:00:34.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.14
p-value of test                       :    0.69


-----------------------------------------------
Normal statistic for number of jumps  : 7.45e-3
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:02:22.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    4.22
p-value of test                       :    0.98


-----------------------------------------------
Normal statistic for number of jumps  :   -0.79
p-value of test                       :    0.78



-----------------------------------------------
CPU time used                    :  00:02:24.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.028
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.16

Tests on the sum of all N observations
Standardized normal statistic         :   -1.62
p-value of test                       :    0.95

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.015
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    : 5.15e-3
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:00:45.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    : 6.69e-3
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:44.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.78
p-value of test                       :    0.56

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.03
p-value of test                       :    0.43

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:23.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  197.56
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:02:06.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.40
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.44
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  209.62
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:02:05.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.61
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10061.35
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:58.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.53

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9880.02
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.32
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:08.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.36
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:06.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   0.081
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:04:16.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.74

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4844.04
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:54.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4833.18
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:53.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4133.49
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:25.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3961.99
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:27.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11813.82
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:31.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11897.24
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:30.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.04
p-value of test                       :    0.70


-----------------------------------------------
Total number of bits:  7999877355

Normal statistic for number of bits   :   -0.97
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.07
p-value of test                       :    0.24


-----------------------------------------------
Total number of bits:  8000064867

Normal statistic for number of bits   :    0.51
p-value of test                       :    0.30



-----------------------------------------------
CPU time used                    :  00:01:09.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.11
p-value of test                       :    0.30

Tests on the sum of all N observations
Standardized normal statistic         :   -0.49
p-value of test                       :    0.69

Sample variance                       :    2.16
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:26.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.041
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

Tests on the sum of all N observations
Standardized normal statistic         :   -2.10
p-value of test                       :    0.98

Sample variance                       :    0.74
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:16.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.52

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Tests on the sum of all N observations
Standardized normal statistic         :    0.24
p-value of test                       :    0.40

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:29.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :   -0.91
p-value of test                       :    0.82

Sample variance                       :    1.16
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:01:16.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:58.78
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 12  CollisionOver, t = 21           0.9999 
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 52527111.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:38.93

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:49.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1346
p-value of test                       :    0.68

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334466
  j =  1                              :        599997308
  j =  2                              :             1346
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.40

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1337
p-value of test                       :    0.76

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334457
  j =  1                              :        599997326
  j =  2                              :             1337
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.93

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.21

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1356
p-value of test                       :    0.58

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334476
  j =  1                              :        599997288
  j =  2                              :             1356
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1392
p-value of test                       :    0.23

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334512
  j =  1                              :        599997216
  j =  2                              :             1392
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.41

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1294
p-value of test                       :    0.97

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334414
  j =  1                              :        599997412
  j =  2                              :             1294
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1306
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334426
  j =  1                              :        599997388
  j =  2                              :             1306
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.72

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1286
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334406
  j =  1                              :        599997428
  j =  2                              :             1286
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5435
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:04:03.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4422
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7378
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:46.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4241
p-value of test                       :    0.93


-----------------------------------------------
CPU time used                    :  00:02:00.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4373
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:02:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7300
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:03:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7250
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:03:09.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7200
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:04:03.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7387
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:04:04.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.57
p-value of test                       :    0.16


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.69
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.68
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     872
p-value of test                       :    0.82

Stat. AD (mNP2)                       :    1.49
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    4.75
p-value of test                       :  3.8e-3

-----------------------------------------------
CPU time used                    :  00:01:49.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.21
p-value of test                       :    0.99

Test on the Nm values of W_{n,i}(mNP1):    1.02
p-value of test                       :    0.34

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     625
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    0.28
p-value of test                       :    0.95

Stat. AD after spacings (mNP2-S)      :    0.94
p-value of test                       :    0.39

-----------------------------------------------
CPU time used                    :  00:01:14.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.44
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.89
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.12
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     318
p-value of test                       :    0.16

Stat. AD (mNP2)                       :    1.89
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:02:14.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.94
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.38
p-value of test                       :    0.86

Test on the Nm values of W_{n,i}(mNP1):    1.70
p-value of test                       :    0.14

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     165
p-value of test                       :    0.12

Stat. AD (mNP2)                       :    0.45
p-value of test                       :    0.80

Stat. AD after spacings (mNP2-S)      :    0.50
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:02:43.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.38
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:55.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.94
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:04.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   17.44
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:58.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.61
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:06.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.00
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.47
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:21.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   51.18
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:21.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   75.45
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  219.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:22.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  456.95
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:48.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1517.24
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:02:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7088.67
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:49.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.029
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.50
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   47.06
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:16.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.083
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    1.94
p-value of test                       :    0.10

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   73.65
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.04
p-value of test                       :    0.96


-----------------------------------------------
CPU time used                    :  00:00:45.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  107.27
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:01:36.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4837.32
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:01:12.88

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:03:18.02

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46224
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870224
  j =  1                              :        399907558
  j =  2                              :            46212
  j =  3                              :                6
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:56.35

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46118
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870118
  j =  1                              :        399907767
  j =  2                              :            46112
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:03.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.65


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:02:32.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.025
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.55
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92


-----------------------------------------------
CPU time used                    :  00:02:24.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.53


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.060
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:01:53.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.077
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    1.80
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.92


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91


-----------------------------------------------
CPU time used                    :  00:02:13.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.29
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:36.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.71e-4
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 1.29e-4
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.27e-4
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    : 5.53e-5
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.65
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.94
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.39
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.89
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:40.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   87.44
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:50.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.92
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   50.70
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.72
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.15
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:00:56.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   45.48
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   37.00
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:46.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   31.07
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:03.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.99
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.38
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.53
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.55
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    3.79
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:01:17.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.23
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :  8.0e-3

Kolmogorov-Smirnov- statistic = D-    :   0.055
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    3.38
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  101.79
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:39.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17385.82
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:00:53.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   42.01
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   48.44
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   28.06
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   26.94
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.31
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:00:37.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   25.70
p-value of test                       :    0.90


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   41.60
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.86
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.71
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   26.26
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  118.17
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  167.62
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  609.59
p-value of test                       :  5.5e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  142.89
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   80.83
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:43.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.12
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.71
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.61
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.46
p-value of test                       :    0.50


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   97.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:00:43.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  416.69
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  417.26
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5188.24
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  376.19
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.33
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.51
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  400.17
p-value of test                       :    0.27


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4994.97
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  369.98
p-value of test                       :    0.61


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.41
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.40
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.86
p-value of test                       :    0.81



-----------------------------------------------
CPU time used                    :  00:02:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.42
p-value of test                       :    0.94


-----------------------------------------------
Normal statistic for number of jumps  :    0.83
p-value of test                       :    0.20



-----------------------------------------------
CPU time used                    :  00:02:24.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

Tests on the sum of all N observations
Standardized normal statistic         :    1.10
p-value of test                       :    0.13

Sample variance                       :    0.84
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:03.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Tests on the sum of all N observations
Standardized normal statistic         :   -0.51
p-value of test                       :    0.69

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.33e-3
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    : 7.38e-3
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    : 8.34e-3
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.58
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:44.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.50
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   12.77
p-value of test                       :    0.12

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:23.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.094
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  205.43
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:02:05.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.41
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  220.06
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:02:05.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10051.54
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:59.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9938.47
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:02.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -1.06
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:08.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.19
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:05.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.71
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:04:15.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.49

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4869.60
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:54.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4868.76
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:53.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4058.99
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:24.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4046.32
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:25.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11770.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:32.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11642.08
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:31.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.56
p-value of test                       :    0.20


-----------------------------------------------
Total number of bits:  8000044938

Normal statistic for number of bits   :    0.36
p-value of test                       :    0.36



-----------------------------------------------
CPU time used                    :  00:01:08.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   68.98
p-value of test                       :    0.08


-----------------------------------------------
Total number of bits:  7999997031

Normal statistic for number of bits   :  -0.023
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:01:09.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.058
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Tests on the sum of all N observations
Standardized normal statistic         :    1.42
p-value of test                       :    0.08

Sample variance                       :    1.00
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:25.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.33
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    1.91
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:16.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    :   0.099
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.82
p-value of test                       :    0.79

Sample variance                       :    0.64
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:28.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.33
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Tests on the sum of all N observations
Standardized normal statistic         :    0.62
p-value of test                       :    0.27

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:16.27

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:08:17.54
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 76  RandomWalk1 J (L=1000, r=0)     5.5e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 53542919.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:02:08.71

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.95


-----------------------------------------------
CPU time used                    :  00:02:09.54

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:38.91

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1406
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334526
  j =  1                              :        599997188
  j =  2                              :             1406
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:02.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1328
p-value of test                       :    0.83

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334448
  j =  1                              :        599997344
  j =  2                              :             1328
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.36

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1302
p-value of test                       :    0.95

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334422
  j =  1                              :        599997396
  j =  2                              :             1302
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:46.61

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.49

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1365
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334485
  j =  1                              :        599997270
  j =  2                              :             1365
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1305
p-value of test                       :    0.94

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334425
  j =  1                              :        599997390
  j =  2                              :             1305
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1310
p-value of test                       :    0.93

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334430
  j =  1                              :        599997380
  j =  2                              :             1310
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5355
p-value of test                       :    0.81


-----------------------------------------------
CPU time used                    :  00:04:03.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4403
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:01:44.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7211
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:02:47.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:02:01.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4251
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:02:01.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:03:09.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7283
p-value of test                       :    0.66


-----------------------------------------------
CPU time used                    :  00:04:01.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7440
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:04:00.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.82
p-value of test                       :    0.46


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.08
p-value of test                       :    0.32

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     880
p-value of test                       :    0.74

Stat. AD (mNP2)                       :    1.04
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:49.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.67
p-value of test                       :    0.14


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.27
p-value of test                       :    0.96

Test on the Nm values of W_{n,i}(mNP1):    2.97
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     663
p-value of test                       :  5.9e-3

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.25
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:14.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.45
p-value of test                       :    0.79


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    2.48
p-value of test                       :    0.05

Test on the Nm values of W_{n,i}(mNP1):    1.19
p-value of test                       :    0.27

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     292
p-value of test                       :    0.66

Stat. AD (mNP2)                       :    0.54
p-value of test                       :    0.70

Stat. AD after spacings (mNP2-S)      :    1.16
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:15.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.63
p-value of test                       :    0.61


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.29
p-value of test                       :    0.94

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     159
p-value of test                       :    0.24

Stat. AD (mNP2)                       :    1.54
p-value of test                       :    0.17

Stat. AD after spacings (mNP2-S)      :    0.56
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:02:40.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   10.74
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:54.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    7.08
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.96
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:57.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   70.39
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:10.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.82
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:20.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   63.83
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:21.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   55.44
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  223.55
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:22.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  407.51
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:47.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1439.62
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7098.80
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   33.60
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:13.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.37
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    1.46
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.13
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:03:08.22

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    6.60
p-value of test                       :    0.25


-----------------------------------------------
CPU time used                    :  00:00:45.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.71
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.27

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5062.95
p-value of test                       :    0.40


-----------------------------------------------
CPU time used                    :  00:01:12.52

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:03:01.32

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45554
p-value of test                       :    0.94


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869554
  j =  1                              :        399908899
  j =  2                              :            45540
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.14

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46042
p-value of test                       :    0.22


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870042
  j =  1                              :        399907917
  j =  2                              :            46040
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.021
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.60
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.95


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.049
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:30.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.056
p-value of test                       :    0.80

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.28


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :   0.092
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.48
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:02:22.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.12


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.053
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:54.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    2.97
p-value of test                       :    0.03

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.98


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:02:11.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.052
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:57.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:18.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.066
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:36.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.33e-4
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    : 1.26e-4
p-value of test                       :    0.53

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:00:23.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.29e-5
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    : 3.20e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    1.05
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:00:23.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.088
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:00:23.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.38
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:39.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.40
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:39.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.28
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:50.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   59.67
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:00:55.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   56.27
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   32.85
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:49.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   62.76
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:00:55.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   33.03
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:55.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   43.85
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:45.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.087
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   33.08
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:03.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   44.74
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:03.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.01
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:26.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.66
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:26.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.41
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:16.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    5.01
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:06.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  145.41
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:38.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.99
p-value of test                       :    0.36

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17518.12
p-value of test                       :    0.32



-----------------------------------------------
CPU time used                    :  00:00:52.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.47
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   30.68
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   30.32
p-value of test                       :    0.21


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   47.60
p-value of test                       :  2.8e-3


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.82
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:37.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   28.99
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   19.76
p-value of test                       :    0.98


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   25.88
p-value of test                       :    0.41


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   33.88
p-value of test                       :    0.09


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   20.20
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:37.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  179.79
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  142.45
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  489.67
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  135.00
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.71
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:43.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.82
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.74
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  487.80
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  136.60
p-value of test                       :    0.47


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   62.11
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  365.67
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.23
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4995.37
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  425.21
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  207.66
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:00:35.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  412.37
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.47
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5074.99
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  407.16
p-value of test                       :    0.14


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.96
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:00:34.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.49
p-value of test                       :    0.13


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



-----------------------------------------------
CPU time used                    :  00:02:21.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   10.30
p-value of test                       :    0.59


-----------------------------------------------
Normal statistic for number of jumps  :   -0.27
p-value of test                       :    0.60



-----------------------------------------------
CPU time used                    :  00:02:22.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Tests on the sum of all N observations
Standardized normal statistic         :    0.44
p-value of test                       :    0.33

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.43
p-value of test                       :    0.02

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    3.62
p-value of test                       :    0.01

Tests on the sum of all N observations
Standardized normal statistic         :   -2.44
p-value of test                       :    0.9927

Sample variance                       :    0.46
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:10.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.85e-3
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.35

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:00:45.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.90e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:44.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.91
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    6.11
p-value of test                       :    0.63

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:24.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.041
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  225.64
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:02:10.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.72

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  214.88
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:02:12.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10100.13
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10001.10
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   0.050
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:01:05.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.43
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:04.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.23
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:04:14.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.45
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 3.53e-3
p-value of test                       :    0.9964

Anderson-Darling statistic = A2       :    3.40
p-value of test                       :    0.02

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4635.30
p-value of test                       :    0.9955

-----------------------------------------------
CPU time used                    :  00:01:52.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.085
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.55

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4978.84
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4095.76
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:26.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3919.58
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:01:24.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11734.36
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:32.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11687.05
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:33.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.50
p-value of test                       :    0.46


-----------------------------------------------
Total number of bits:  7999976388

Normal statistic for number of bits   :   -0.19
p-value of test                       :    0.57



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   51.91
p-value of test                       :    0.56


-----------------------------------------------
Total number of bits:  8000135637

Normal statistic for number of bits   :    1.07
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:06.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.57

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Tests on the sum of all N observations
Standardized normal statistic         :   -0.45
p-value of test                       :    0.67

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:25.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.15
p-value of test                       :    0.28

Tests on the sum of all N observations
Standardized normal statistic         :   -1.19
p-value of test                       :    0.88

Sample variance                       :    0.75
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:16.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.030
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.18

Tests on the sum of all N observations
Standardized normal statistic         :   -1.57
p-value of test                       :    0.94

Sample variance                       :    0.93
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:01:27.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.080
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.74

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    1.04
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:01:13.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:15.73

 All tests were passed




Server wird beendet - Lösche Semaphor 54558727.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:40.78

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.06


-----------------------------------------------
CPU time used                    :  00:00:50.31

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1299
p-value of test                       :    0.96

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334419
  j =  1                              :        599997402
  j =  2                              :             1299
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.46

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.60

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.33

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1380
p-value of test                       :    0.34

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334500
  j =  1                              :        599997240
  j =  2                              :             1380
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1290
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334410
  j =  1                              :        599997420
  j =  2                              :             1290
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.76

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1369
p-value of test                       :    0.45

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334489
  j =  1                              :        599997262
  j =  2                              :             1369
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5588
p-value of test                       :    0.01


-----------------------------------------------
CPU time used                    :  00:04:00.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4405
p-value of test                       :    0.15


-----------------------------------------------
CPU time used                    :  00:01:41.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7348
p-value of test                       :    0.37


-----------------------------------------------
CPU time used                    :  00:02:45.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4195
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:02:01.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4346
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:02.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:03:13.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7381
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:11.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7280
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:04:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7389
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:03:59.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.51
p-value of test                       :    0.17


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.17
p-value of test                       :    0.28

Test on the Nm values of W_{n,i}(mNP1):    1.00
p-value of test                       :    0.36

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     950
p-value of test                       :    0.05

Stat. AD (mNP2)                       :    0.53
p-value of test                       :    0.71

Stat. AD after spacings (mNP2-S)      :    0.55
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:49.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.03
p-value of test                       :    0.34


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.92
p-value of test                       :    0.40

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     597
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    1.26
p-value of test                       :    0.24

Stat. AD after spacings (mNP2-S)      :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.87
p-value of test                       :    0.43


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.66
p-value of test                       :    0.59

Test on the Nm values of W_{n,i}(mNP1):    0.66
p-value of test                       :    0.59

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     314
p-value of test                       :    0.22

Stat. AD (mNP2)                       :    0.61
p-value of test                       :    0.64

Stat. AD after spacings (mNP2-S)      :    1.42
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:12.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.91
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     155
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:02:41.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    6.43
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:55.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.03
p-value of test                       :    0.96

-----------------------------------------------
CPU time used                    :  00:01:04.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   16.70
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:58.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.50
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:06.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.14
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:09.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.37
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:20.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   50.68
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:20.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   34.77
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:21.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  228.94
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:22.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  451.86
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:47.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1603.13
p-value of test                       :  1.4e-3

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7033.74
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:49.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   26.33
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   47.17
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:03:09.06

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    5.73
p-value of test                       :    0.33


-----------------------------------------------
CPU time used                    :  00:00:45.51

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  119.46
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5041.43
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:01:12.39

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:55.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45837
p-value of test                       :    0.58


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869837
  j =  1                              :        399908330
  j =  2                              :            45829
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.06

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45984
p-value of test                       :    0.31


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869984
  j =  1                              :        399908034
  j =  2                              :            45980
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:58.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.25
p-value of test                       :    0.97

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.77

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:02:30.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.30

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.029
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.16
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:22.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :   0.095
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.64


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.048
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:01:55.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.042
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.84


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.68

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76


-----------------------------------------------
CPU time used                    :  00:02:09.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.076
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:56.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.51

Anderson-Darling statistic = A2       :    1.00
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:36.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.34e-5
p-value of test                       :    0.9928

Kolmogorov-Smirnov- statistic = D-    : 1.39e-4
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.87
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.64e-4
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    : 6.90e-5
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.53
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:00:23.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -3.11
p-value of test                       :    0.9991    *****

-----------------------------------------------
CPU time used                    :  00:00:23.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.24
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:00:23.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.31
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:44.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.84
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:42.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.31
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:00:50.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   66.59
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:56.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   45.26
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   58.87
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   38.47
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:56.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   35.73
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   39.78
p-value of test                       :    0.09

-----------------------------------------------
CPU time used                    :  00:01:46.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.086
p-value of test                       :    0.82

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   36.08
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   39.08
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:02.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.93
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:25.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.22
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:16.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:06.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.079
p-value of test                       :    0.84

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  140.86
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:38.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.78
p-value of test                       :    0.49

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17302.02
p-value of test                       :    0.75



-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   31.86
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   26.74
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.40
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.48
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.24
p-value of test                       :    0.51


-----------------------------------------------
CPU time used                    :  00:00:36.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   53.82
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   53.03
p-value of test                       :    0.03


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   22.20
p-value of test                       :    0.62


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.05
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.35
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:36.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  127.85
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  165.45
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  454.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.50
p-value of test                       :    0.20


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   60.70
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:43.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.02
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.82
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  618.38
p-value of test                       :  2.3e-4    *****


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  108.43
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.31
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  404.73
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  343.32
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4846.18
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  397.68
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  183.48
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:34.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  382.04
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  338.84
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4975.73
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  368.18
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  181.02
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:00:34.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    2.41
p-value of test                       :    0.9985


-----------------------------------------------
Normal statistic for number of jumps  :   -0.10
p-value of test                       :    0.54



-----------------------------------------------
CPU time used                    :  00:02:21.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    9.48
p-value of test                       :    0.66


-----------------------------------------------
Normal statistic for number of jumps  :  -0.037
p-value of test                       :    0.51



-----------------------------------------------
CPU time used                    :  00:02:21.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.55
p-value of test                       :  1.2e-3

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    5.29
p-value of test                       :  2.2e-3

Tests on the sum of all N observations
Standardized normal statistic         :   -2.71
p-value of test                       :    0.9966

Sample variance                       :    0.63
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:08.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.56

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :   0.054
p-value of test                       :    0.48

Sample variance                       :    1.29
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:11.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.19e-3
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:00:45.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.45e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:00:44.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.60
p-value of test                       :    0.47

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:26.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.44
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:22.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.09

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.89

Anderson-Darling statistic = A2       :    1.40
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  170.41
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:02:05.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.72
p-value of test                       :    0.54

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  210.94
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:02:07.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9949.74
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.50
p-value of test                       :  3.7e-3

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    4.69
p-value of test                       :  4.3e-3

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9701.20
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:02.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:06.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.078
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -1.21
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:04:15.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4827.49
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:52.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.56
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4733.80
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:54.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4191.18
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:24.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4062.73
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:26.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11964.39
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:31.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11807.84
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:01:31.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   58.23
p-value of test                       :    0.32


-----------------------------------------------
Total number of bits:  7999905846

Normal statistic for number of bits   :   -0.74
p-value of test                       :    0.77



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   64.02
p-value of test                       :    0.17


-----------------------------------------------
Total number of bits:  8000092713

Normal statistic for number of bits   :    0.73
p-value of test                       :    0.23



-----------------------------------------------
CPU time used                    :  00:01:07.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.61
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Tests on the sum of all N observations
Standardized normal statistic         :   -0.14
p-value of test                       :    0.55

Sample variance                       :    1.36
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:01:15.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.63

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Tests on the sum of all N observations
Standardized normal statistic         :    0.57
p-value of test                       :    0.29

Sample variance                       :    1.51
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:27.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.39
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.48

Anderson-Darling statistic = A2       :    2.90
p-value of test                       :    0.03

Tests on the sum of all N observations
Standardized normal statistic         :   -1.38
p-value of test                       :    0.92

Sample variance                       :    3.07
p-value of test                       :  1.1e-3

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:34.70
 The following tests gave p-values outside [0.001, 0.9990]:
 (eps  means a value < 1.0e-300):
 (eps1 means a value < 1.0e-15):

       Test                          p-value
 ----------------------------------------------
 55  SampleCorr, k = 1               0.9991 
 77  RandomWalk1 J (L=1000, r=20)    2.3e-4
 ----------------------------------------------
 All other tests were passed




Server wird beendet - Lösche Semaphor 55640071.
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                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:40.46

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.63


-----------------------------------------------
CPU time used                    :  00:00:50.07

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1374
p-value of test                       :    0.40

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334494
  j =  1                              :        599997252
  j =  2                              :             1374
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1373
p-value of test                       :    0.41

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334493
  j =  1                              :        599997254
  j =  2                              :             1373
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.80

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1325
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334445
  j =  1                              :        599997350
  j =  2                              :             1325
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1376
p-value of test                       :    0.38

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334496
  j =  1                              :        599997248
  j =  2                              :             1376
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.13

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1331
p-value of test                       :    0.81

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334451
  j =  1                              :        599997338
  j =  2                              :             1331
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.75

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1371
p-value of test                       :    0.43

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334491
  j =  1                              :        599997258
  j =  2                              :             1371
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.27

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:18.48

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1277
p-value of test                       :    0.9911

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334397
  j =  1                              :        599997446
  j =  2                              :             1277
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:44.79

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.98

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1336
p-value of test                       :    0.77

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334456
  j =  1                              :        599997328
  j =  2                              :             1336
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5516
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:04:00.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4420
p-value of test                       :    0.10


-----------------------------------------------
CPU time used                    :  00:01:44.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7372
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:46.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4326
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4389
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:02:03.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7386
p-value of test                       :    0.22


-----------------------------------------------
CPU time used                    :  00:03:14.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7302
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:03:14.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7423
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:04:10.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7343
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:04:13.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.69


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.05
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    1.52
p-value of test                       :    0.17

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     877
p-value of test                       :    0.77

Stat. AD (mNP2)                       :    1.32
p-value of test                       :    0.23

Stat. AD after spacings (mNP2-S)      :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:50.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.40
p-value of test                       :    0.20


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.83
p-value of test                       :    0.11

Test on the Nm values of W_{n,i}(mNP1):    1.41
p-value of test                       :    0.20

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     594
p-value of test                       :    0.59

Stat. AD (mNP2)                       :    1.13
p-value of test                       :    0.29

Stat. AD after spacings (mNP2-S)      :    0.37
p-value of test                       :    0.88

-----------------------------------------------
CPU time used                    :  00:01:15.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.39
p-value of test                       :    0.85


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.76
p-value of test                       :    0.51

Test on the Nm values of W_{n,i}(mNP1):    0.56
p-value of test                       :    0.68

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     285
p-value of test                       :    0.80

Stat. AD (mNP2)                       :    1.05
p-value of test                       :    0.33

Stat. AD after spacings (mNP2-S)      :    0.54
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:02:14.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.48
p-value of test                       :    0.76


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.34
p-value of test                       :    0.90

Test on the Nm values of W_{n,i}(mNP1):    0.32
p-value of test                       :    0.92

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     153
p-value of test                       :    0.41

Stat. AD (mNP2)                       :    1.48
p-value of test                       :    0.18

Stat. AD after spacings (mNP2-S)      :    2.51
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:02:40.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.44
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:00:57.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   16.26
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:06.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:00.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   25.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:12.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   62.16
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:14.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   66.72
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.36
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   35.90
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:26.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  227.01
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:01:30.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  475.07
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:58.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1476.92
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:02:06.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7173.35
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:59.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.61

Kolmogorov-Smirnov- statistic = D-    :    0.35
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.70

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   31.16
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:18.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 2.21e-5
p-value of test                       : 1 -  2.2e-5    *****

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   92.12
p-value of test                       :  4.8e-3

-----------------------------------------------
CPU time used                    :  00:03:26.69

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    4.54
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:46.38

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :   92.39
p-value of test                       :    0.97


-----------------------------------------------
CPU time used                    :  00:01:43.96

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4981.40
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:01:26.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.24


-----------------------------------------------
CPU time used                    :  00:02:55.50

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46193
p-value of test                       :    0.07


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870193
  j =  1                              :        399907616
  j =  2                              :            46189
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:51.38

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45808
p-value of test                       :    0.63


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869808
  j =  1                              :        399908388
  j =  2                              :            45800
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.081
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.27


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :   0.051
p-value of test                       :    0.78

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:02:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.21
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.014
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:02:24.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.66
p-value of test                       :    0.59

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.47


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.95
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:57.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.57


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.013
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:02:16.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.76

-----------------------------------------------
CPU time used                    :  00:01:56.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.55
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:19.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.97
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:37.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.23e-4
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    : 1.41e-4
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.82e-4
p-value of test                       :    0.27

Kolmogorov-Smirnov- statistic = D-    : 1.23e-4
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.79
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:24.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -1.31
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.30
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:00:23.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.95
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:44.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.63
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:01:45.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.13
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:00:49.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.38
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:56.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   61.00
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   42.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:49.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   28.28
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:58.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   36.67
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:57.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   24.89
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:51.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.37
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.69
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:03.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.44
p-value of test                       :    0.01

Kolmogorov-Smirnov- statistic = D-    : 5.48e-3
p-value of test                       :    0.9942

Anderson-Darling statistic = A2       :    1.85
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   25.33
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:03.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.53
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:26.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.87
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:26.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.76
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:16.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:07.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.39
p-value of test                       :    0.86

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  124.81
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:43.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.61

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17348.00
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:00:53.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   48.82
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   35.58
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.21
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   22.58
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.18
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:00:37.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   47.04
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   31.04
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.56
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   28.03
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    6.02
p-value of test                       :    0.9930


-----------------------------------------------
CPU time used                    :  00:00:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  155.69
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  160.90
p-value of test                       :    0.19


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  485.04
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  117.71
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   70.16
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:43.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  119.42
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  170.24
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  510.11
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  143.99
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   92.84
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:42.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  376.74
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  371.13
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4899.17
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.77
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  176.97
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:00:34.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  374.29
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  398.46
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4913.20
p-value of test                       :    0.81


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  361.71
p-value of test                       :    0.72


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  179.40
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:34.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.02
p-value of test                       :    0.53


-----------------------------------------------
Normal statistic for number of jumps  :   0.048
p-value of test                       :    0.48



-----------------------------------------------
CPU time used                    :  00:02:22.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.80
p-value of test                       :    0.46


-----------------------------------------------
Normal statistic for number of jumps  :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:02:24.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.55

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.84

Tests on the sum of all N observations
Standardized normal statistic         :    0.23
p-value of test                       :    0.41

Sample variance                       :    0.65
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:05.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :   0.098
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.64
p-value of test                       :    0.74

Sample variance                       :    1.23
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.31

Kolmogorov-Smirnov- statistic = D-    : 7.11e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

-----------------------------------------------
CPU time used                    :  00:00:46.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 7.12e-3
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.07

Anderson-Darling statistic = A2       :    1.13
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:00:44.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.57
p-value of test                       :    0.48

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:26.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    7.15
p-value of test                       :    0.52

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:24.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.60

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  202.45
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:06.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.093
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.28
p-value of test                       :    0.95

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  196.02
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:02:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.83

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9985.71
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:57.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.48
p-value of test                       :  6.3e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    3.78
p-value of test                       :    0.01

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9668.20
p-value of test                       :    0.9911

-----------------------------------------------
CPU time used                    :  00:01:02.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.91
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:13.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.41
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:09.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.30
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:04:33.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.54
p-value of test                       :    0.71

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4881.41
p-value of test                       :    0.53

-----------------------------------------------
CPU time used                    :  00:01:51.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.57

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.47

Anderson-Darling statistic = A2       :    0.50
p-value of test                       :    0.75

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4889.08
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:55.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4111.68
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:22.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3952.86
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:24.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11728.46
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:31.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :12149.93
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:34.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   59.57
p-value of test                       :    0.28


-----------------------------------------------
Total number of bits:  8000099736

Normal statistic for number of bits   :    0.79
p-value of test                       :    0.22



-----------------------------------------------
CPU time used                    :  00:01:15.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   54.61
p-value of test                       :    0.45


-----------------------------------------------
Total number of bits:  8000193513

Normal statistic for number of bits   :    1.53
p-value of test                       :    0.06



-----------------------------------------------
CPU time used                    :  00:01:10.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.88
p-value of test                       :    0.42

Tests on the sum of all N observations
Standardized normal statistic         :   -0.12
p-value of test                       :    0.55

Sample variance                       :    0.29
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.031
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.65
p-value of test                       :    0.15

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    0.86
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.070
p-value of test                       :    0.87

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Tests on the sum of all N observations
Standardized normal statistic         :   -0.48
p-value of test                       :    0.68

Sample variance                       :    1.01
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:01:26.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.21
p-value of test                       :    0.42

Sample variance                       :    0.53
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:21.28

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:18.77

 All tests were passed




Server wird beendet - Lösche Semaphor 56655879.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:00:39.79

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:50.59

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:36.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1322
p-value of test                       :    0.87

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334442
  j =  1                              :        599997356
  j =  2                              :             1322
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:01.26

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.00

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1352
p-value of test                       :    0.62

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334472
  j =  1                              :        599997296
  j =  2                              :             1352
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.10

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1313
p-value of test                       :    0.92

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334433
  j =  1                              :        599997374
  j =  2                              :             1313
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1340
p-value of test                       :    0.74

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334460
  j =  1                              :        599997320
  j =  2                              :             1340
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:45.47

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1423
p-value of test                       :    0.06

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334543
  j =  1                              :        599997154
  j =  2                              :             1423
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:19.56

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1334
p-value of test                       :    0.79

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334454
  j =  1                              :        599997332
  j =  2                              :             1334
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:43.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.77

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1446
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334566
  j =  1                              :        599997108
  j =  2                              :             1446
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5378
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:04:01.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4449
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:01:43.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7303
p-value of test                       :    0.57


-----------------------------------------------
CPU time used                    :  00:02:47.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:01.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4431
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:02:02.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7394
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:03:12.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7219
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:03:12.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7262
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:04:07.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7359
p-value of test                       :    0.32


-----------------------------------------------
CPU time used                    :  00:04:09.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.79
p-value of test                       :    0.49

Test on the Nm values of W_{n,i}(mNP1):    0.25
p-value of test                       :    0.97

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     896
p-value of test                       :    0.54

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:51.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.52
p-value of test                       :    0.72


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.00
p-value of test                       :    0.35

Test on the Nm values of W_{n,i}(mNP1):    0.50
p-value of test                       :    0.75

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     591
p-value of test                       :    0.63

Stat. AD (mNP2)                       :    0.56
p-value of test                       :    0.68

Stat. AD after spacings (mNP2-S)      :    1.27
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:16.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.00
p-value of test                       :    0.09


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.40
p-value of test                       :    0.84

Test on the Nm values of W_{n,i}(mNP1):    0.59
p-value of test                       :    0.65

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     296
p-value of test                       :    0.58

Stat. AD (mNP2)                       :    1.16
p-value of test                       :    0.28

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:19.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.43
p-value of test                       :    0.81


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.86
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.77
p-value of test                       :    0.50

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    0.75
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:46.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    8.23
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:00:57.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.33
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:07.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.46
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:01.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   23.79
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.15
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:11.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   45.53
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:25.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   49.75
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.01
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  245.82
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:28.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  460.82
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1480.86
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6931.48
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:56.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.052
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.43
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   39.35
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:17.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.31
p-value of test                       :    0.93

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   54.76
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:03:20.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    7.50
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:00:47.11

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  118.21
p-value of test                       :    0.50


-----------------------------------------------
CPU time used                    :  00:01:43.50

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 4946.37
p-value of test                       :    0.82


-----------------------------------------------
CPU time used                    :  00:01:25.07

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:03:20.25

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45693
p-value of test                       :    0.81


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869693
  j =  1                              :        399908614
  j =  2                              :            45693
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.43

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46123
p-value of test                       :    0.13


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870123
  j =  1                              :        399907757
  j =  2                              :            46117
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:02.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.044
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    1.43
p-value of test                       :    0.19

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.94


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88


-----------------------------------------------
CPU time used                    :  00:02:34.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.25

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.44


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:29.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.83

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.68


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.013
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    1.19
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:01:53.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.76


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.067
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.78


-----------------------------------------------
CPU time used                    :  00:02:09.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.58

Kolmogorov-Smirnov- statistic = D-    :   0.072
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:56.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.27

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:19.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :   0.056
p-value of test                       :    0.85

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:01:38.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.28e-5
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    : 1.52e-4
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.96e-5
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    : 9.10e-5
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.26
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:00:24.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    3.02
p-value of test                       :  1.3e-3

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -0.95
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:41.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.29
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:42.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   71.65
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:00:50.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.92
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   76.69
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.98
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:52.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   24.34
p-value of test                       :    0.95

-----------------------------------------------
CPU time used                    :  00:00:59.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.11
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:00:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   33.70
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:53.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.53

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.22
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   38.00
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:02.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :   0.053
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.23
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.79
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:01:26.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.18
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:27.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.59
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:17.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.19
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:08.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.30
p-value of test                       :    0.14

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.26

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  114.73
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:00:43.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :   0.040
p-value of test                       :    0.94

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.81
p-value of test                       :    0.12

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17755.43
p-value of test                       :    0.04



-----------------------------------------------
CPU time used                    :  00:00:53.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   41.26
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   43.71
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   34.37
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   37.26
p-value of test                       :    0.04


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   23.18
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:00:37.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   51.23
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   38.87
p-value of test                       :    0.30


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   19.68
p-value of test                       :    0.76


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.07
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   12.45
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:37.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  151.35
p-value of test                       :    0.36


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.57
p-value of test                       :    0.74


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  466.69
p-value of test                       :    0.85


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  116.27
p-value of test                       :    0.89


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.91
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:00:45.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  157.81
p-value of test                       :    0.24


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  141.65
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  492.52
p-value of test                       :    0.59


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  114.78
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.89
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:00:44.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  431.36
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  392.59
p-value of test                       :    0.37


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4967.51
p-value of test                       :    0.63


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  350.83
p-value of test                       :    0.84


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  227.31
p-value of test                       :    0.09


-----------------------------------------------
CPU time used                    :  00:00:36.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  388.58
p-value of test                       :    0.43


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  351.63
p-value of test                       :    0.88


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5038.49
p-value of test                       :    0.35


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  335.13
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  203.33
p-value of test                       :    0.42


-----------------------------------------------
CPU time used                    :  00:00:35.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   19.80
p-value of test                       :    0.07


-----------------------------------------------
Normal statistic for number of jumps  :    0.11
p-value of test                       :    0.46



-----------------------------------------------
CPU time used                    :  00:02:24.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    6.86
p-value of test                       :    0.87


-----------------------------------------------
Normal statistic for number of jumps  :    0.50
p-value of test                       :    0.31



-----------------------------------------------
CPU time used                    :  00:02:23.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :   0.012
p-value of test                       :    0.99

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

Tests on the sum of all N observations
Standardized normal statistic         :   -1.83
p-value of test                       :    0.97

Sample variance                       :    0.96
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.82

Tests on the sum of all N observations
Standardized normal statistic         :   -0.30
p-value of test                       :    0.62

Sample variance                       :    0.72
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:06.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.63e-3
p-value of test                       :    0.54

Kolmogorov-Smirnov- statistic = D-    : 6.20e-3
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.89

-----------------------------------------------
CPU time used                    :  00:00:44.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    : 7.02e-3
p-value of test                       :    0.66

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:00:43.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.20
p-value of test                       :    0.41

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:23.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   11.43
p-value of test                       :    0.18

-----------------------------------------------
Global longest run of 1               :   33.00
p-value of test                       :    0.44



-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.74

Kolmogorov-Smirnov- statistic = D-    :    0.32
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.17
p-value of test                       :    0.28

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  218.79
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:02:06.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.23
p-value of test                       :    0.98

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  199.47
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:02:06.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.70
p-value of test                       :    0.56

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10104.26
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:59.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.61

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.58

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9980.50
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:04.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.40
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:10.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.82
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:07.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.86
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:04:32.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.024
p-value of test                       :    0.97

Kolmogorov-Smirnov- statistic = D-    :    0.31
p-value of test                       :    0.11

Anderson-Darling statistic = A2       :    1.54
p-value of test                       :    0.17

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 5051.73
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:01:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.27
p-value of test                       :    0.19

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.68

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4873.16
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:58.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4225.30
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:25.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4074.02
p-value of test                       :    0.68

-----------------------------------------------
CPU time used                    :  00:01:27.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.91
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:34.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11889.45
p-value of test                       :    0.34

-----------------------------------------------
CPU time used                    :  00:01:37.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   48.39
p-value of test                       :    0.69


-----------------------------------------------
Total number of bits:  7999964265

Normal statistic for number of bits   :   -0.28
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:01:05.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   40.71
p-value of test                       :    0.91


-----------------------------------------------
Total number of bits:  8000030799

Normal statistic for number of bits   :    0.24
p-value of test                       :    0.40



-----------------------------------------------
CPU time used                    :  00:01:06.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Tests on the sum of all N observations
Standardized normal statistic         :   -0.27
p-value of test                       :    0.61

Sample variance                       :    1.73
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.70
p-value of test                       :    0.24

Sample variance                       :    0.75
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.050
p-value of test                       :    0.92

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :   -0.73
p-value of test                       :    0.77

Sample variance                       :    1.02
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:27.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.26

Anderson-Darling statistic = A2       :    0.80
p-value of test                       :    0.48

Tests on the sum of all N observations
Standardized normal statistic         :    0.74
p-value of test                       :    0.23

Sample variance                       :    0.42
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:19.79

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:11:25.94

 All tests were passed




Server wird beendet - Lösche Semaphor 57769991.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:00:39.24

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:50.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.15

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1330
p-value of test                       :    0.82

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334450
  j =  1                              :        599997340
  j =  2                              :             1330
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.87

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1366
p-value of test                       :    0.48

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334486
  j =  1                              :        599997268
  j =  2                              :             1366
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.42

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1377
p-value of test                       :    0.37

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334497
  j =  1                              :        599997246
  j =  2                              :             1377
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:17.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1354
p-value of test                       :    0.60

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334474
  j =  1                              :        599997292
  j =  2                              :             1354
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1353
p-value of test                       :    0.61

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334473
  j =  1                              :        599997294
  j =  2                              :             1353
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:16.92

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1390
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334510
  j =  1                              :        599997220
  j =  2                              :             1390
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.71

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1444
p-value of test                       :    0.02

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334564
  j =  1                              :        599997112
  j =  2                              :             1444
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1436
p-value of test                       :    0.03

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334556
  j =  1                              :        599997128
  j =  2                              :             1436
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5476
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:04:01.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4344
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:01:44.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7412
p-value of test                       :    0.14


-----------------------------------------------
CPU time used                    :  00:02:45.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4391
p-value of test                       :    0.21


-----------------------------------------------
CPU time used                    :  00:02:01.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4300
p-value of test                       :    0.71


-----------------------------------------------
CPU time used                    :  00:02:02.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7437
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:13.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7279
p-value of test                       :    0.67


-----------------------------------------------
CPU time used                    :  00:03:10.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7345
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:04:07.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7339
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:04:10.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.42
p-value of test                       :    0.82


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.34
p-value of test                       :    0.90

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     901
p-value of test                       :    0.49

Stat. AD (mNP2)                       :    1.07
p-value of test                       :    0.32

Stat. AD after spacings (mNP2-S)      :    0.77
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:47.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.55
p-value of test                       :    0.70


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.70
p-value of test                       :    0.55

Test on the Nm values of W_{n,i}(mNP1):    0.61
p-value of test                       :    0.64

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    0.70
p-value of test                       :    0.56

Stat. AD after spacings (mNP2-S)      :    1.57
p-value of test                       :    0.16

-----------------------------------------------
CPU time used                    :  00:01:14.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    3.68
p-value of test                       :    0.01


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.68
p-value of test                       :    0.57

Test on the Nm values of W_{n,i}(mNP1):    1.13
p-value of test                       :    0.30

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     303
p-value of test                       :    0.44

Stat. AD (mNP2)                       :    1.03
p-value of test                       :    0.34

Stat. AD after spacings (mNP2-S)      :    0.87
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:02:13.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.64


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.04
p-value of test                       :    0.33

Test on the Nm values of W_{n,i}(mNP1):    3.01
p-value of test                       :    0.03

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     169
p-value of test                       :    0.07

Stat. AD (mNP2)                       :    0.71
p-value of test                       :    0.55

Stat. AD after spacings (mNP2-S)      :    0.51
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:02:39.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   12.64
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:00:57.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :   11.73
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:06.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   13.37
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:01.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :    8.71
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:01:09.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   59.43
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:13.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   65.84
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:01:26.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   39.65
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:26.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.15
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:26.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  273.82
p-value of test                       :    0.03

-----------------------------------------------
CPU time used                    :  00:01:29.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  418.23
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:56.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1578.50
p-value of test                       :  5.1e-3

-----------------------------------------------
CPU time used                    :  00:02:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7038.76
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:01:57.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   24.46
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   52.15
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:03:21.67

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.92
p-value of test                       :    0.86


-----------------------------------------------
CPU time used                    :  00:00:48.30

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  127.19
p-value of test                       :    0.29


-----------------------------------------------
CPU time used                    :  00:01:43.57

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5060.83
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:01:24.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.44


-----------------------------------------------
CPU time used                    :  00:03:19.39

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45799
p-value of test                       :    0.65


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869799
  j =  1                              :        399908407
  j =  2                              :            45789
  j =  3                              :                5
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:54.23

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    46234
p-value of test                       :    0.05


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165870234
  j =  1                              :        399907535
  j =  2                              :            46228
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:59.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.034
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.064
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.21
p-value of test                       :    0.99


-----------------------------------------------
CPU time used                    :  00:02:32.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.033
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.01

Anderson-Darling statistic = A2       :    2.75
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.04


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.070
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    0.71
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:02:21.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    : 8.60e-3
p-value of test                       :    0.99

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.12

Anderson-Darling statistic = A2       :    1.24
p-value of test                       :    0.25

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.06


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    3.23
p-value of test                       :    0.02


-----------------------------------------------
CPU time used                    :  00:01:52.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    0.37
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.13

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:02:08.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    1.52
p-value of test                       :    0.17

-----------------------------------------------
CPU time used                    :  00:01:56.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.092
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.56
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:19.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:37.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.00e-4
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    : 2.85e-4
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:00:23.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 9.25e-5
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    : 1.13e-4
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:24.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.10
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :    0.70
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:00:24.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.13
p-value of test                       :    0.55

-----------------------------------------------
CPU time used                    :  00:01:43.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.58
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:44.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   67.91
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:52.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.90
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:00:59.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   60.50
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:00:59.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   46.81
p-value of test                       :    0.13

-----------------------------------------------
CPU time used                    :  00:00:52.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:00.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   37.51
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:00.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   34.67
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:51.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   47.67
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:03.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.63

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   32.34
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:04.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.30
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:01:27.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.54
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:01:27.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    2.34
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:17.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.27
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:07.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  142.49
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:00:41.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :   0.088
p-value of test                       :    0.81

Anderson-Darling statistic = A2       :    0.74
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17277.91
p-value of test                       :    0.79



-----------------------------------------------
CPU time used                    :  00:00:53.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   40.92
p-value of test                       :    0.26


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   39.37
p-value of test                       :    0.28


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   29.44
p-value of test                       :    0.25


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   18.61
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.50
p-value of test                       :    0.49


-----------------------------------------------
CPU time used                    :  00:00:37.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   29.16
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   22.76
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   18.94
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   35.60
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :    8.89
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:37.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  162.38
p-value of test                       :    0.17


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  121.16
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  514.28
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  121.93
p-value of test                       :    0.80


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   51.99
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:00:44.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  138.40
p-value of test                       :    0.66


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  154.00
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  512.48
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  106.68
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   81.31
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:00:43.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  370.79
p-value of test                       :    0.68


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  380.42
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5165.91
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  390.01
p-value of test                       :    0.32


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  200.69
p-value of test                       :    0.47


-----------------------------------------------
CPU time used                    :  00:00:35.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  418.34
p-value of test                       :    0.11


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  399.25
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5041.94
p-value of test                       :    0.34


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  374.62
p-value of test                       :    0.54


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  186.60
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:00:35.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   15.56
p-value of test                       :    0.21


-----------------------------------------------
Normal statistic for number of jumps  :   -0.53
p-value of test                       :    0.70



-----------------------------------------------
CPU time used                    :  00:02:23.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    8.34
p-value of test                       :    0.76


-----------------------------------------------
Normal statistic for number of jumps  :    0.90
p-value of test                       :    0.18



-----------------------------------------------
CPU time used                    :  00:02:23.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

Tests on the sum of all N observations
Standardized normal statistic         :    0.43
p-value of test                       :    0.33

Sample variance                       :    0.66
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:01:04.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    1.32
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.40
p-value of test                       :    0.65

Sample variance                       :    2.38
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:07.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.010
p-value of test                       :    0.42

Kolmogorov-Smirnov- statistic = D-    : 3.51e-3
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.46
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:45.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.014
p-value of test                       :    0.20

Kolmogorov-Smirnov- statistic = D-    : 9.22e-3
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    1.20
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:00:45.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   16.44
p-value of test                       :    0.04

-----------------------------------------------
Global longest run of 1               :   31.00
p-value of test                       :    0.69



-----------------------------------------------
CPU time used                    :  00:01:25.52

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.78
p-value of test                       :    0.78

-----------------------------------------------
Global longest run of 1               :   34.00
p-value of test                       :    0.25



-----------------------------------------------
CPU time used                    :  00:01:23.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.090
p-value of test                       :    0.81

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  216.29
p-value of test                       :    0.20

-----------------------------------------------
CPU time used                    :  00:02:06.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    1.90
p-value of test                       :    0.11

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  200.25
p-value of test                       :    0.48

-----------------------------------------------
CPU time used                    :  00:02:05.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.60

Anderson-Darling statistic = A2       :    0.43
p-value of test                       :    0.81

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9948.73
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:00:59.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.47
p-value of test                       :    0.77

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9960.30
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:03.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.52
p-value of test                       :    0.30

-----------------------------------------------
CPU time used                    :  00:01:10.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    0.93
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:08.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    0.26
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:04:34.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.086
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.76
p-value of test                       :    0.51

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4953.12
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:54.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.068
p-value of test                       :    0.88

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4781.93
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:58.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4115.90
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4066.15
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:27.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11783.99
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:34.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11963.49
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:37.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.99
p-value of test                       :    0.33


-----------------------------------------------
Total number of bits:  8000025993

Normal statistic for number of bits   :    0.21
p-value of test                       :    0.42



-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   52.27
p-value of test                       :    0.54


-----------------------------------------------
Total number of bits:  8000034612

Normal statistic for number of bits   :    0.27
p-value of test                       :    0.39



-----------------------------------------------
CPU time used                    :  00:01:07.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.64

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.31

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.56

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.71
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:24.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.57
p-value of test                       :    0.67

Tests on the sum of all N observations
Standardized normal statistic         :   -0.55
p-value of test                       :    0.71

Sample variance                       :    0.56
p-value of test                       :    0.83

-----------------------------------------------
CPU time used                    :  00:01:17.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.077
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    1.34
p-value of test                       :    0.22

Tests on the sum of all N observations
Standardized normal statistic         :    1.31
p-value of test                       :    0.09

Sample variance                       :    1.34
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:26.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.42
p-value of test                       :    0.83

Tests on the sum of all N observations
Standardized normal statistic         :    0.49
p-value of test                       :    0.31

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:18.87

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:10:53.15

 All tests were passed




Server wird beendet - Lösche Semaphor 58818567.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:00:40.50

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.77


-----------------------------------------------
CPU time used                    :  00:00:50.09

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1402
p-value of test                       :    0.16

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334522
  j =  1                              :        599997196
  j =  2                              :             1402
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.44

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1389
p-value of test                       :    0.25

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334509
  j =  1                              :        599997222
  j =  2                              :             1389
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:58.19

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.70

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1362
p-value of test                       :    0.52

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334482
  j =  1                              :        599997276
  j =  2                              :             1362
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.64

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1355
p-value of test                       :    0.59

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334475
  j =  1                              :        599997290
  j =  2                              :             1355
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.51

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1363
p-value of test                       :    0.51

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334483
  j =  1                              :        599997274
  j =  2                              :             1363
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.03

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1397
p-value of test                       :    0.19

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334517
  j =  1                              :        599997206
  j =  2                              :             1397
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.55

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1318
p-value of test                       :    0.89

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334438
  j =  1                              :        599997364
  j =  2                              :             1318
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1326
p-value of test                       :    0.85

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334446
  j =  1                              :        599997348
  j =  2                              :             1326
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.24

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1348
p-value of test                       :    0.66

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334468
  j =  1                              :        599997304
  j =  2                              :             1348
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5371
p-value of test                       :    0.75


-----------------------------------------------
CPU time used                    :  00:04:00.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4263
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:01:42.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7263
p-value of test                       :    0.74


-----------------------------------------------
CPU time used                    :  00:02:43.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4328
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:01:58.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4317
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:01:58.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7269
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:03:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7220
p-value of test                       :    0.87


-----------------------------------------------
CPU time used                    :  00:03:08.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7361
p-value of test                       :    0.31


-----------------------------------------------
CPU time used                    :  00:04:00.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7400
p-value of test                       :    0.17


-----------------------------------------------
CPU time used                    :  00:04:01.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.29
p-value of test                       :    0.94


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.25
p-value of test                       :    0.25

Test on the Nm values of W_{n,i}(mNP1):    0.88
p-value of test                       :    0.43

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     947
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    1.40
p-value of test                       :    0.20

Stat. AD after spacings (mNP2-S)      :    0.69
p-value of test                       :    0.57

-----------------------------------------------
CPU time used                    :  00:01:46.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.73
p-value of test                       :    0.13


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.39
p-value of test                       :    0.21

Test on the Nm values of W_{n,i}(mNP1):    0.63
p-value of test                       :    0.62

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     613
p-value of test                       :    0.30

Stat. AD (mNP2)                       :    1.83
p-value of test                       :    0.11

Stat. AD after spacings (mNP2-S)      :    1.91
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:13.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.50
p-value of test                       :    0.18


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.65
p-value of test                       :    0.60

Test on the Nm values of W_{n,i}(mNP1):    2.09
p-value of test                       :    0.08

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     327
p-value of test                       :    0.06

Stat. AD (mNP2)                       :    0.50
p-value of test                       :    0.75

Stat. AD after spacings (mNP2-S)      :    1.61
p-value of test                       :    0.15

-----------------------------------------------
CPU time used                    :  00:02:12.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.85
p-value of test                       :    0.44


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.66

Test on the Nm values of W_{n,i}(mNP1):    0.68
p-value of test                       :    0.58

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     156
p-value of test                       :    0.32

Stat. AD (mNP2)                       :    0.34
p-value of test                       :    0.90

Stat. AD after spacings (mNP2-S)      :    0.16
p-value of test                       :    0.9972

-----------------------------------------------
CPU time used                    :  00:02:39.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    2.70
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:55.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    9.63
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:03.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   20.93
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   22.33
p-value of test                       :    0.22

-----------------------------------------------
CPU time used                    :  00:01:07.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   56.42
p-value of test                       :    0.38

-----------------------------------------------
CPU time used                    :  00:01:12.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   48.80
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:21.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   60.64
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:21.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   67.16
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:21.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  243.40
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:23.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  449.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:47.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1324.99
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:02:04.76

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 6806.30
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.47
p-value of test                       :    0.08

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    1.48
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.30
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.07

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.35
p-value of test                       :    0.21

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   48.00
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:03:09.56

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.57
p-value of test                       :    0.90


-----------------------------------------------
CPU time used                    :  00:00:45.25

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  105.94
p-value of test                       :    0.80


-----------------------------------------------
CPU time used                    :  00:01:36.75

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5096.70
p-value of test                       :    0.28


-----------------------------------------------
CPU time used                    :  00:01:12.31

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.30


-----------------------------------------------
CPU time used                    :  00:03:16.81

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45978
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869978
  j =  1                              :        399908045
  j =  2                              :            45976
  j =  3                              :                1
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:52.64

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45942
p-value of test                       :    0.39


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869942
  j =  1                              :        399908118
  j =  2                              :            45938
  j =  3                              :                2
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:00.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.48

Kolmogorov-Smirnov- statistic = D-    :   0.032
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.65
p-value of test                       :    0.60

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.75


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.30

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.90
p-value of test                       :    0.41


-----------------------------------------------
CPU time used                    :  00:02:31.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.037
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.16
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.09
p-value of test                       :    0.31

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.11


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.074
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    2.47
p-value of test                       :    0.05


-----------------------------------------------
CPU time used                    :  00:02:25.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.087
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.15

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.65

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.29


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.11

Kolmogorov-Smirnov- statistic = D-    :   0.024
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    2.22
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:53.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :   0.079
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.69


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.091
p-value of test                       :    0.68

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.13

Anderson-Darling statistic = A2       :    1.42
p-value of test                       :    0.20


-----------------------------------------------
CPU time used                    :  00:02:06.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.097
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :   0.096
p-value of test                       :    0.45

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:56.07

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.028
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.18

Anderson-Darling statistic = A2       :    1.83
p-value of test                       :    0.11

-----------------------------------------------
CPU time used                    :  00:01:18.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.096
p-value of test                       :    0.65

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:36.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 4.76e-5
p-value of test                       :    0.91

Kolmogorov-Smirnov- statistic = D-    : 2.22e-4
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    1.22
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:00:23.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.50e-5
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    : 3.05e-4
p-value of test                       :    0.02

Anderson-Darling statistic = A2       :    2.53
p-value of test                       :    0.05

-----------------------------------------------
CPU time used                    :  00:00:24.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :    0.24
p-value of test                       :    0.40

-----------------------------------------------
CPU time used                    :  00:00:23.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   -1.33
p-value of test                       :    0.91

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.32
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:40.42

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -1.08
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:41.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   62.58
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:00:50.46

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   51.45
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:00:56.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   54.90
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:56.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.30
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:00:50.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.83
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   29.87
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   30.17
p-value of test                       :    0.41

-----------------------------------------------
CPU time used                    :  00:01:46.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.71
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:03.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.36
p-value of test                       :    0.88

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   34.25
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:03.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    4.21
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:26.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    2.38
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:25.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.17
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:16.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.50
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:07.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.62

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  129.11
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.40

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.59

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17378.57
p-value of test                       :    0.61



-----------------------------------------------
CPU time used                    :  00:00:53.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.12
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   34.12
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   37.14
p-value of test                       :    0.06


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.53
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   13.89
p-value of test                       :    0.68


-----------------------------------------------
CPU time used                    :  00:00:37.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   43.65
p-value of test                       :    0.18


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   28.09
p-value of test                       :    0.79


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   16.19
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   17.37
p-value of test                       :    0.83


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   15.63
p-value of test                       :    0.55


-----------------------------------------------
CPU time used                    :  00:00:36.98

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  174.61
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  152.86
p-value of test                       :    0.33


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  499.92
p-value of test                       :    0.49


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  132.00
p-value of test                       :    0.58


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :  111.75
p-value of test                       :  3.0e-3


-----------------------------------------------
CPU time used                    :  00:00:44.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  140.94
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.62
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  458.50
p-value of test                       :    0.91


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  155.04
p-value of test                       :    0.13


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   66.12
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:00:43.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  424.34
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  397.20
p-value of test                       :    0.31


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4731.31
p-value of test                       :    0.9968


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  352.27
p-value of test                       :    0.82


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  196.36
p-value of test                       :    0.56


-----------------------------------------------
CPU time used                    :  00:00:36.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  378.27
p-value of test                       :    0.57


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  386.90
p-value of test                       :    0.45


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5053.95
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  410.55
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  229.87
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:36.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   17.30
p-value of test                       :    0.14


-----------------------------------------------
Normal statistic for number of jumps  :  -0.064
p-value of test                       :    0.53



-----------------------------------------------
CPU time used                    :  00:02:24.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   13.18
p-value of test                       :    0.36


-----------------------------------------------
Normal statistic for number of jumps  :    1.36
p-value of test                       :    0.09



-----------------------------------------------
CPU time used                    :  00:02:24.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.70

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.70

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :    0.14
p-value of test                       :    0.44

Sample variance                       :    0.66
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:04.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.33
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :    0.21
p-value of test                       :    0.37

Anderson-Darling statistic = A2       :    2.21
p-value of test                       :    0.07

Tests on the sum of all N observations
Standardized normal statistic         :   -1.01
p-value of test                       :    0.84

Sample variance                       :    2.28
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:01:07.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.91e-3
p-value of test                       :    0.75

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.44

Anderson-Darling statistic = A2       :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:00:44.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    : 2.20e-3
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

-----------------------------------------------
CPU time used                    :  00:00:43.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    4.94
p-value of test                       :    0.76

-----------------------------------------------
Global longest run of 1               :   30.00
p-value of test                       :    0.90



-----------------------------------------------
CPU time used                    :  00:01:25.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.47
p-value of test                       :    0.71

-----------------------------------------------
Global longest run of 1               :   36.00
p-value of test                       :    0.07



-----------------------------------------------
CPU time used                    :  00:01:22.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.28

Kolmogorov-Smirnov- statistic = D-    :   0.094
p-value of test                       :    0.79

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  193.74
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:02:06.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.46
p-value of test                       :  8.7e-3

Kolmogorov-Smirnov- statistic = D-    :   0.058
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.66
p-value of test                       :    0.04

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  165.32
p-value of test                       :    0.97

-----------------------------------------------
CPU time used                    :  00:02:07.87

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.082
p-value of test                       :    0.83

Kolmogorov-Smirnov- statistic = D-    :    0.30
p-value of test                       :    0.14

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10093.55
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:00:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.017
p-value of test                       :    0.98

Kolmogorov-Smirnov- statistic = D-    :    0.34
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.73
p-value of test                       :    0.13

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  :10248.94
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:02.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    0.39
p-value of test                       :    0.35

-----------------------------------------------
CPU time used                    :  00:01:08.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:07.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :    1.99
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:04:21.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.86

Anderson-Darling statistic = A2       :    1.29
p-value of test                       :    0.23

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4785.17
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:54.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.67

Kolmogorov-Smirnov- statistic = D-    :    0.29
p-value of test                       :    0.16

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.41

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4943.63
p-value of test                       :    0.29

-----------------------------------------------
CPU time used                    :  00:01:54.17

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3925.75
p-value of test                       :    0.98

-----------------------------------------------
CPU time used                    :  00:01:26.03

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4094.59
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:25.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11923.34
p-value of test                       :    0.26

-----------------------------------------------
CPU time used                    :  00:01:31.56

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11932.18
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:32.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000001

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   62.79
p-value of test                       :    0.19


-----------------------------------------------
Total number of bits:  7999943910

Normal statistic for number of bits   :   -0.44
p-value of test                       :    0.67



-----------------------------------------------
CPU time used                    :  00:01:06.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   46.18
p-value of test                       :    0.77


-----------------------------------------------
Total number of bits:  7999931325

Normal statistic for number of bits   :   -0.54
p-value of test                       :    0.71



-----------------------------------------------
CPU time used                    :  00:01:07.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.46

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.64

Anderson-Darling statistic = A2       :    0.49
p-value of test                       :    0.75

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    1.70
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:25.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.060
p-value of test                       :    0.90

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.19

Anderson-Darling statistic = A2       :    1.27
p-value of test                       :    0.24

Tests on the sum of all N observations
Standardized normal statistic         :    1.37
p-value of test                       :    0.09

Sample variance                       :    0.62
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:14.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.24
p-value of test                       :    0.26

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.29

Anderson-Darling statistic = A2       :    1.31
p-value of test                       :    0.23

Tests on the sum of all N observations
Standardized normal statistic         :   -0.10
p-value of test                       :    0.54

Sample variance                       :    2.32
p-value of test                       :    0.01

-----------------------------------------------
CPU time used                    :  00:01:26.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    1.36
p-value of test                       :    0.21

Tests on the sum of all N observations
Standardized normal statistic         :   -1.39
p-value of test                       :    0.92

Sample variance                       :    1.80
p-value of test                       :    0.06

-----------------------------------------------
CPU time used                    :  00:01:15.10

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:15.62

 All tests were passed




Server wird beendet - Lösche Semaphor 59932679.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.79


-----------------------------------------------
CPU time used                    :  00:00:39.35

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:00:50.12

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1403
p-value of test                       :    0.15

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334523
  j =  1                              :        599997194
  j =  2                              :             1403
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:35.65

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1391
p-value of test                       :    0.24

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334511
  j =  1                              :        599997218
  j =  2                              :             1391
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:59.69

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1364
p-value of test                       :    0.50

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334484
  j =  1                              :        599997272
  j =  2                              :             1364
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.25

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1404
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334524
  j =  1                              :        599997192
  j =  2                              :             1404
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.83

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1475
p-value of test                       :  1.6e-3

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334595
  j =  1                              :        599997050
  j =  2                              :             1475
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.99

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1271
p-value of test                       :    0.9944

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334391
  j =  1                              :        599997458
  j =  2                              :             1271
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:15.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1358
p-value of test                       :    0.56

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334478
  j =  1                              :        599997284
  j =  2                              :             1358
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:41.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1272
p-value of test                       :    0.9939

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334392
  j =  1                              :        599997456
  j =  2                              :             1272
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.29

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1360
p-value of test                       :    0.54

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334480
  j =  1                              :        599997280
  j =  2                              :             1360
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:38.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5376
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:04:01.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4356
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:01:43.19

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7405
p-value of test                       :    0.16


-----------------------------------------------
CPU time used                    :  00:02:44.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4340
p-value of test                       :    0.48


-----------------------------------------------
CPU time used                    :  00:01:59.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4435
p-value of test                       :    0.07


-----------------------------------------------
CPU time used                    :  00:01:59.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7383
p-value of test                       :    0.23


-----------------------------------------------
CPU time used                    :  00:03:09.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7234
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:03:08.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7138
p-value of test                       :    0.98


-----------------------------------------------
CPU time used                    :  00:04:02.01

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7395
p-value of test                       :    0.19


-----------------------------------------------
CPU time used                    :  00:04:02.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.27
p-value of test                       :    0.96


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    1.63
p-value of test                       :    0.15

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     850
p-value of test                       :    0.95

Stat. AD (mNP2)                       :    0.24
p-value of test                       :    0.98

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:48.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.60
p-value of test                       :    0.65


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.83
p-value of test                       :    0.46

Test on the Nm values of W_{n,i}(mNP1):    0.33
p-value of test                       :    0.91

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     590
p-value of test                       :    0.65

Stat. AD (mNP2)                       :    0.42
p-value of test                       :    0.83

Stat. AD after spacings (mNP2-S)      :    0.38
p-value of test                       :    0.87

-----------------------------------------------
CPU time used                    :  00:01:15.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.96
p-value of test                       :    0.38


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.35
p-value of test                       :    0.89

Test on the Nm values of W_{n,i}(mNP1):    0.20
p-value of test                       :    0.99

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     301
p-value of test                       :    0.48

Stat. AD (mNP2)                       :    0.92
p-value of test                       :    0.40

Stat. AD after spacings (mNP2-S)      :    0.40
p-value of test                       :    0.85

-----------------------------------------------
CPU time used                    :  00:02:15.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.99
p-value of test                       :    0.10


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.56
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.60

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.73
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    1.70
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:43.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.03
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:54.57

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    5.02
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:02.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   14.33
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:00:57.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   11.69
p-value of test                       :    0.86

-----------------------------------------------
CPU time used                    :  00:01:05.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   58.73
p-value of test                       :    0.31

-----------------------------------------------
CPU time used                    :  00:01:12.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.97
p-value of test                       :    0.74

-----------------------------------------------
CPU time used                    :  00:01:20.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   44.98
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:21.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   53.32
p-value of test                       :    0.50

-----------------------------------------------
CPU time used                    :  00:01:21.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  212.29
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:01:22.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.72
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1368.21
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:02:04.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7183.09
p-value of test                       :    0.12

-----------------------------------------------
CPU time used                    :  00:01:50.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.45
p-value of test                       :    0.09

Anderson-Darling statistic = A2       :    1.68
p-value of test                       :    0.14

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   45.35
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:01:17.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.06

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.65

Anderson-Darling statistic = A2       :    1.63
p-value of test                       :    0.15

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   44.80
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:03:08.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    1.30
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:44.81

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  123.25
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:35.97

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5104.60
p-value of test                       :    0.26


-----------------------------------------------
CPU time used                    :  00:01:13.17

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.08


-----------------------------------------------
CPU time used                    :  00:03:21.97

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45996
p-value of test                       :    0.29


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869996
  j =  1                              :        399908012
  j =  2                              :            45988
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.00

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45428
p-value of test                       :    0.98


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869428
  j =  1                              :        399909151
  j =  2                              :            45414
  j =  3                              :                7
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:05:01.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    :   0.054
p-value of test                       :    0.77

Anderson-Darling statistic = A2       :    0.81
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.80


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.042
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45


-----------------------------------------------
CPU time used                    :  00:02:31.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.078
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.62
p-value of test                       :    0.63

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.34


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.58


-----------------------------------------------
CPU time used                    :  00:02:25.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.050
p-value of test                       :    0.87

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.22

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.52

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.17


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.43

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.58

Anderson-Darling statistic = A2       :    0.51
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:01:54.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.22
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.043
p-value of test                       :    0.91

Anderson-Darling statistic = A2       :    1.39
p-value of test                       :    0.20

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.89


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.56

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.53
p-value of test                       :    0.72


-----------------------------------------------
CPU time used                    :  00:02:06.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.04

Kolmogorov-Smirnov- statistic = D-    :   0.033
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    2.10
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:55.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.75
p-value of test                       :    0.51

-----------------------------------------------
CPU time used                    :  00:01:18.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.03

Kolmogorov-Smirnov- statistic = D-    :   0.066
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.47
p-value of test                       :    0.18

-----------------------------------------------
CPU time used                    :  00:01:35.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.96e-4
p-value of test                       :    0.22

Kolmogorov-Smirnov- statistic = D-    : 8.55e-5
p-value of test                       :    0.75

Anderson-Darling statistic = A2       :    0.73
p-value of test                       :    0.54

-----------------------------------------------
CPU time used                    :  00:00:23.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 1.65e-4
p-value of test                       :    0.34

Kolmogorov-Smirnov- statistic = D-    : 2.92e-4
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.68
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:24.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 1


-----------------------------------------------
Normal statistic                      :   -0.76
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:00:23.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


-----------------------------------------------
Normal statistic                      :   0.034
p-value of test                       :    0.49

-----------------------------------------------
CPU time used                    :  00:00:23.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    0.59
p-value of test                       :    0.28

-----------------------------------------------
CPU time used                    :  00:01:39.43

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :    1.27
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:40.89

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   68.37
p-value of test                       :    0.43

-----------------------------------------------
CPU time used                    :  00:00:49.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   72.01
p-value of test                       :    0.32

-----------------------------------------------
CPU time used                    :  00:00:56.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


-----------------------------------------------
Number of degrees of freedom          :   67
Chi-square statistic                  :   92.52
p-value of test                       :    0.02

-----------------------------------------------
CPU time used                    :  00:00:55.77

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   39.42
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:00:49.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   34.00
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:00:55.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   53.76
p-value of test                       :    0.04

-----------------------------------------------
CPU time used                    :  00:00:55.81

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


-----------------------------------------------
Number of degrees of freedom          :   29
Chi-square statistic                  :   25.94
p-value of test                       :    0.63

-----------------------------------------------
CPU time used                    :  00:01:45.09

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.32
p-value of test                       :    0.10

Kolmogorov-Smirnov- statistic = D-    :   0.015
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.18
p-value of test                       :    0.27

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   28.00
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:04.14

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.25
p-value of test                       :    0.23

Kolmogorov-Smirnov- statistic = D-    :   0.061
p-value of test                       :    0.90

Anderson-Darling statistic = A2       :    0.85
p-value of test                       :    0.44

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   29.14
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:01:04.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    3.24
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:27.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    1.39
p-value of test                       :    0.71

-----------------------------------------------
CPU time used                    :  00:01:26.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    0.66
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:01:16.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    1.03
p-value of test                       :    0.60

-----------------------------------------------
CPU time used                    :  00:01:07.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.19
p-value of test                       :    0.44

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  118.97
p-value of test                       :    0.75

-----------------------------------------------
CPU time used                    :  00:00:39.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.36
p-value of test                       :    0.05

Kolmogorov-Smirnov- statistic = D-    :   0.034
p-value of test                       :    0.95

Anderson-Darling statistic = A2       :    1.58
p-value of test                       :    0.16

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17157.33
p-value of test                       :    0.93



-----------------------------------------------
CPU time used                    :  00:00:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   23.47
p-value of test                       :    0.95


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   32.20
p-value of test                       :    0.60


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   21.39
p-value of test                       :    0.67


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.01
p-value of test                       :    0.64


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.97
p-value of test                       :    0.46


-----------------------------------------------
CPU time used                    :  00:00:37.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   27.03
p-value of test                       :    0.86


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   45.02
p-value of test                       :    0.12


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.29
p-value of test                       :    0.73


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   14.16
p-value of test                       :    0.94


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   11.20
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:00:37.12

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.03
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  158.51
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  545.39
p-value of test                       :    0.08


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  126.47
p-value of test                       :    0.71


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   59.48
p-value of test                       :    0.89


-----------------------------------------------
CPU time used                    :  00:00:44.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  134.07
p-value of test                       :    0.75


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  150.64
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  523.19
p-value of test                       :    0.23


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  128.99
p-value of test                       :    0.65


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   72.10
p-value of test                       :    0.54


-----------------------------------------------
CPU time used                    :  00:00:43.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  362.60
p-value of test                       :    0.78


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  379.00
p-value of test                       :    0.56


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 5056.13
p-value of test                       :    0.29


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  328.87
p-value of test                       :    0.97


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  204.75
p-value of test                       :    0.39


-----------------------------------------------
CPU time used                    :  00:00:35.61

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  420.31
p-value of test                       :    0.10


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  369.68
p-value of test                       :    0.69


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4925.97
p-value of test                       :    0.77


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  398.65
p-value of test                       :    0.22


-----------------------------------------------
Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  170.26
p-value of test                       :    0.94


-----------------------------------------------
CPU time used                    :  00:00:35.26

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :   11.13
p-value of test                       :    0.52


-----------------------------------------------
Normal statistic for number of jumps  :  -0.046
p-value of test                       :    0.52



-----------------------------------------------
CPU time used                    :  00:02:24.45

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.10
p-value of test                       :    0.85


-----------------------------------------------
Normal statistic for number of jumps  :   -0.22
p-value of test                       :    0.59



-----------------------------------------------
CPU time used                    :  00:02:25.06

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.17

Kolmogorov-Smirnov- statistic = D-    :   0.040
p-value of test                       :    0.94

Anderson-Darling statistic = A2       :    1.02
p-value of test                       :    0.35

Tests on the sum of all N observations
Standardized normal statistic         :   -1.25
p-value of test                       :    0.89

Sample variance                       :    0.71
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:05.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.16
p-value of test                       :    0.55

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.92
p-value of test                       :    0.40

Tests on the sum of all N observations
Standardized normal statistic         :    0.77
p-value of test                       :    0.22

Sample variance                       :    0.39
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:07.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.011
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    0.59
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:00:45.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 6.44e-3
p-value of test                       :    0.71

Kolmogorov-Smirnov- statistic = D-    :   0.011
p-value of test                       :    0.34

Anderson-Darling statistic = A2       :    0.84
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:00:44.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :   14.77
p-value of test                       :    0.06

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    2.16
p-value of test                       :    0.98

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.66

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  198.32
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:02:06.20

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.051
p-value of test                       :    0.92

Kolmogorov-Smirnov- statistic = D-    :    0.26
p-value of test                       :    0.23

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  221.72
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:02:05.32

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.16

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.72

Anderson-Darling statistic = A2       :    0.93
p-value of test                       :    0.39

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9869.06
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:59.60

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.41

Kolmogorov-Smirnov- statistic = D-    :    0.11
p-value of test                       :    0.73

Anderson-Darling statistic = A2       :    0.32
p-value of test                       :    0.92

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9959.22
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:02.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :    1.44
p-value of test                       :    0.07

-----------------------------------------------
CPU time used                    :  00:01:07.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :   0.086
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:04.85

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :   -0.78
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:04:17.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.28
p-value of test                       :    0.18

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.98

Anderson-Darling statistic = A2       :    1.26
p-value of test                       :    0.24

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4750.39
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:54.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.24
p-value of test                       :    0.28

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4968.40
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:57.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4235.15
p-value of test                       :    0.10

-----------------------------------------------
CPU time used                    :  00:01:24.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4189.59
p-value of test                       :    0.21

-----------------------------------------------
CPU time used                    :  00:01:25.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11873.59
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:32.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.21
p-value of test                       :    0.47

-----------------------------------------------
CPU time used                    :  00:01:31.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   61.42
p-value of test                       :    0.23


-----------------------------------------------
Total number of bits:  7999880556

Normal statistic for number of bits   :   -0.94
p-value of test                       :    0.83



-----------------------------------------------
CPU time used                    :  00:01:06.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   39.44
p-value of test                       :    0.93


-----------------------------------------------
Total number of bits:  7999953627

Normal statistic for number of bits   :   -0.37
p-value of test                       :    0.64



-----------------------------------------------
CPU time used                    :  00:01:07.29

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.46

Anderson-Darling statistic = A2       :    0.45
p-value of test                       :    0.80

Tests on the sum of all N observations
Standardized normal statistic         :    0.76
p-value of test                       :    0.22

Sample variance                       :    1.09
p-value of test                       :    0.37

-----------------------------------------------
CPU time used                    :  00:01:26.55

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.073
p-value of test                       :    0.86

Kolmogorov-Smirnov- statistic = D-    :    0.28
p-value of test                       :    0.17

Anderson-Darling statistic = A2       :    1.03
p-value of test                       :    0.34

Tests on the sum of all N observations
Standardized normal statistic         :    1.11
p-value of test                       :    0.13

Sample variance                       :    0.55
p-value of test                       :    0.84

-----------------------------------------------
CPU time used                    :  00:01:15.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.046
p-value of test                       :    0.93

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.03

Anderson-Darling statistic = A2       :    2.09
p-value of test                       :    0.08

Tests on the sum of all N observations
Standardized normal statistic         :    1.69
p-value of test                       :    0.05

Sample variance                       :    0.38
p-value of test                       :    0.94

-----------------------------------------------
CPU time used                    :  00:01:27.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.10
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.27
p-value of test                       :    0.20

Anderson-Darling statistic = A2       :    0.86
p-value of test                       :    0.44

Tests on the sum of all N observations
Standardized normal statistic         :    0.68
p-value of test                       :    0.25

Sample variance                       :    1.10
p-value of test                       :    0.36

-----------------------------------------------
CPU time used                    :  00:01:15.17

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:07:27.72

 All tests were passed




Server wird beendet - Lösche Semaphor 60981255.
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
                 Starting BigCrush
                 Version: TestU01 1.2.3
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  0,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.84


-----------------------------------------------
CPU time used                    :  00:00:39.67

Generator state:




***********************************************************
Test smarsa_SerialOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 22,   d =  256,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =           16777216
       Expected number per cell =   59.604645
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0083558402,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 16711680
Value of the statistic                : 1.67e+7
p-value of test                       :    0.27


-----------------------------------------------
CPU time used                    :  00:00:50.53

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1426
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334546
  j =  1                              :        599997148
  j =  2                              :             1426
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:02:37.86

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  9,   d = 2097152,   t =  2,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1449
p-value of test                       :    0.01

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334569
  j =  1                              :        599997102
  j =  2                              :             1449
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:00.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1284
p-value of test                       :    0.99

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334404
  j =  1                              :        599997432
  j =  2                              :             1284
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.05

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 16,   d = 16384,   t =  3,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1407
p-value of test                       :    0.13

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334527
  j =  1                              :        599997186
  j =  2                              :             1407
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:40.97

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1291
p-value of test                       :    0.98

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334411
  j =  1                              :        599997418
  j =  2                              :             1291
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:14.22

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 24,   d =   64,   t =  7,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:42.23

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1405
p-value of test                       :    0.14

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334525
  j =  1                              :        599997190
  j =  2                              :             1405
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:13.90

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 27,   d =    8,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1394
p-value of test                       :    0.21

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334514
  j =  1                              :        599997212
  j =  2                              :             1394
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:39.73

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r =  0,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1425
p-value of test                       :    0.05

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334545
  j =  1                              :        599997150
  j =  2                              :             1425
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:11.82

Generator state:




***********************************************************
Test smarsa_CollisionOver calling smultin_MultinomialOver

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_MultinomialOver test:
-----------------------------------------------
   N = 30,  n = 20000000,  r = 28,   d =    4,   t = 21,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellSerial
       Number of cells = d^t =      4398046511104
       Expected number per cell =  1 /  219902.33
       EColl = n^2 / (2k) =  45.47473509
       Hashing =   TRUE

       Collision test

       CollisionOver:   density = n / k =  1 /  219902.33
       Expected number of collisions = Mu =      45.47


-----------------------------------------------
Results of CollisionOver test:

POISSON approximation                 :
Expected number of collisions = N*Mu  :     1364.24
Observed number of collisions         :     1386
p-value of test                       :    0.28

-----------------------------
Total number of cells containing j balls

  j =  0                              :  131940795334506
  j =  1                              :        599997228
  j =  2                              :             1386
  j =  3                              :                0
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:03:37.90

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 100,  n = 10000000,  r =  0,    d = 2147483648,    t = 2,    p = 1


      Number of cells = d^t = 4611686018427387904
      Lambda = Poisson mean =      54.2101


----------------------------------------------------
Total expected number = N*Lambda      :    5421.01
Total observed number                 :    5384
p-value of test                       :    0.69


-----------------------------------------------
CPU time used                    :  00:04:02.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 2097152,    t = 3,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4273
p-value of test                       :    0.83


-----------------------------------------------
CPU time used                    :  00:01:43.34

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 65536,    t = 4,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7272
p-value of test                       :    0.70


-----------------------------------------------
CPU time used                    :  00:02:45.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4349
p-value of test                       :    0.43


-----------------------------------------------
CPU time used                    :  00:01:59.86

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  7,    d = 512,    t = 7,    p = 1


      Number of cells = d^t = 9223372036854775808
      Lambda = Poisson mean =     216.8404


----------------------------------------------------
Total expected number = N*Lambda      :    4336.81
Total observed number                 :    4452
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:02:00.73

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 14,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7425
p-value of test                       :    0.11


-----------------------------------------------
CPU time used                    :  00:03:11.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 22,    d = 256,    t = 8,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7398
p-value of test                       :    0.18


-----------------------------------------------
CPU time used                    :  00:03:09.38

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r =  0,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7353
p-value of test                       :    0.34


-----------------------------------------------
CPU time used                    :  00:04:01.48

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_BirthdaySpacings test:
-----------------------------------------------
   N = 20,  n = 30000000,  r = 26,    d = 16,    t = 16,    p = 1


      Number of cells = d^t = 18446744073709551616
      Lambda = Poisson mean =     365.9182


----------------------------------------------------
Total expected number = N*Lambda      :    7318.36
Total observed number                 :    7297
p-value of test                       :    0.60


-----------------------------------------------
CPU time used                    :  00:04:04.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 30,  n = 6000000,  r =  0,  t = 3,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    2.22
p-value of test                       :    0.07


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    1.22
p-value of test                       :    0.26

Test on the Nm values of W_{n,i}(mNP1):    0.49
p-value of test                       :    0.76

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     900
Number of jumps of Y                  :     892
p-value of test                       :    0.60

Stat. AD (mNP2)                       :    0.62
p-value of test                       :    0.63

Stat. AD after spacings (mNP2-S)      :    1.26
p-value of test                       :    0.25

-----------------------------------------------
CPU time used                    :  00:01:48.78

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 20,  n = 4000000,  r =  0,  t = 5,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.38
p-value of test                       :    0.87


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.58
p-value of test                       :    0.67

Test on the Nm values of W_{n,i}(mNP1):    0.65
p-value of test                       :    0.61

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     600
Number of jumps of Y                  :     587
p-value of test                       :    0.69

Stat. AD (mNP2)                       :    0.43
p-value of test                       :    0.82

Stat. AD after spacings (mNP2-S)      :    1.05
p-value of test                       :    0.33

-----------------------------------------------
CPU time used                    :  00:01:15.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N = 10,  n = 3000000,  r =  0,  t = 9,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    0.50
p-value of test                       :    0.75


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.96
p-value of test                       :    0.38

Test on the Nm values of W_{n,i}(mNP1):    0.97
p-value of test                       :    0.37

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     300
Number of jumps of Y                  :     307
p-value of test                       :    0.35

Stat. AD (mNP2)                       :    2.09
p-value of test                       :    0.08

Stat. AD after spacings (mNP2-S)      :    0.89
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:02:16.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


snpair_ClosePairs test:
-----------------------------------------------
   N =  5,  n = 2000000,  r =  0,  t = 16,  p = 0,  m = 30,  Torus =  TRUE


---------------------------------------
Test based on the 2 nearest points (NP):

Stat. AD on the N values (NP)         :    1.30
p-value of test                       :    0.23


A2 test based on the spacings between the
   successive jump times of process Y_n(t):

A2 test on the values of A2 (m-NP)    :    0.87
p-value of test                       :    0.43

Test on the Nm values of W_{n,i}(mNP1):    0.51
p-value of test                       :    0.73

Test on the jump times of Y
   (superposition of Yn):

Expected number of jumps of Y = mN    :     150
Number of jumps of Y                  :     140
p-value of test                       :    0.78

Stat. AD (mNP2)                       :    0.72
p-value of test                       :    0.54

Stat. AD after spacings (mNP2-S)      :    0.53
p-value of test                       :    0.72

-----------------------------------------------
CPU time used                    :  00:02:43.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r =  0,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    3.61
p-value of test                       :    0.82

-----------------------------------------------
CPU time used                    :  00:00:55.27

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 400000000,  r = 27,   d =    8,   k =    8


-----------------------------------------------
Number of degrees of freedom          :    7
Chi-square statistic                  :    4.68
p-value of test                       :    0.70

-----------------------------------------------
CPU time used                    :  00:01:03.05

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   15.19
p-value of test                       :    0.65

-----------------------------------------------
CPU time used                    :  00:00:57.92

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_SimpPoker test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   d =   32,   k =   32


-----------------------------------------------
Number of degrees of freedom          :   18
Chi-square statistic                  :   18.27
p-value of test                       :    0.44

-----------------------------------------------
CPU time used                    :  00:01:06.71

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r =  0,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.41
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:09.75

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 10,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   54.68
p-value of test                       :    0.45

-----------------------------------------------
CPU time used                    :  00:01:21.82

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 20,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   61.00
p-value of test                       :    0.24

-----------------------------------------------
CPU time used                    :  00:01:21.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_CouponCollector test:
-----------------------------------------------
   N =  1,  n = 200000000,  r = 27,   d =    8


-----------------------------------------------
Number of degrees of freedom          :   54
Chi-square statistic                  :   46.09
p-value of test                       :    0.77

-----------------------------------------------
CPU time used                    :  00:01:21.65

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   Alpha =        0,   Beta  =   0.0625


-----------------------------------------------
Number of degrees of freedom          :  232
Chi-square statistic                  :  244.59
p-value of test                       :    0.27

-----------------------------------------------
CPU time used                    :  00:01:22.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 300000000,  r = 25,   Alpha =        0,   Beta  =  0.03125


-----------------------------------------------
Number of degrees of freedom          :  434
Chi-square statistic                  :  409.96
p-value of test                       :    0.79

-----------------------------------------------
CPU time used                    :  00:01:46.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   Alpha =        0,   Beta  = 0.0078125


-----------------------------------------------
Number of degrees of freedom          : 1437
Chi-square statistic                  : 1319.74
p-value of test                       :    0.99

-----------------------------------------------
CPU time used                    :  00:02:04.22

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Gap test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   Alpha =        0,   Beta  = 0.000976562


-----------------------------------------------
Number of degrees of freedom          : 7046
Chi-square statistic                  : 7214.47
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:01:49.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N =  5,  n = 1000000000,  r =  0,   Up = FALSE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.35
p-value of test                       :    0.24

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.67
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          :   30
Chi-square statistic                  :   23.08
p-value of test                       :    0.81

-----------------------------------------------
CPU time used                    :  00:01:14.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_Run test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 15,   Up =  TRUE


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.23
p-value of test                       :    0.29

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.41

Anderson-Darling statistic = A2       :    1.04
p-value of test                       :    0.34

Test on the sum of all N observations
Number of degrees of freedom          :   60
Chi-square statistic                  :   56.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:03:08.80

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  3,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                  6
       Expected number per cell =  1.6666667e+08
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  2.5000002e-09,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :    5
Value of the statistic                :    3.58
p-value of test                       :    0.61


-----------------------------------------------
CPU time used                    :  00:00:44.36

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r =  5,   t =  5,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =                120
       Expected number per cell =   8333333.3
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.9500005e-08,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          :  119
Value of the statistic                :  122.90
p-value of test                       :    0.38


-----------------------------------------------
CPU time used                    :  00:01:36.23

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  5,   t =  7,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =               5040
       Expected number per cell =   99206.349
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =  5.0390004e-06,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 5039
Value of the statistic                : 5218.47
p-value of test                       :    0.04


-----------------------------------------------
CPU time used                    :  00:01:13.14

Generator state:




***********************************************************
Test sknuth_Permutation calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N =  1,  n = 500000000,  r = 10,   t = 10,
       Sparse =  FALSE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =            3628800
       Expected number per cell =    137.7866
       Hashing =  FALSE

   For Delta > -1, we use the ChiSquare approximation
   Correction factor of the ChiSquare: 
       Delta =     1,    Mu =   0.0036287993,    Sigma =          1

-----------------------------------------------
Test Results for Delta =   1.0000

Number of degrees of freedom          : 3628799
Value of the statistic                : 3.63e+6
p-value of test                       :    0.85


-----------------------------------------------
CPU time used                    :  00:03:22.27

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r =  0,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45983
p-value of test                       :    0.32


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869983
  j =  1                              :        399908038
  j =  2                              :            45975
  j =  3                              :                4
  j =  4                              :                0
  j =  5                              :                0

-----------------------------------------------
CPU time used                    :  00:04:53.93

Generator state:




***********************************************************
Test sknuth_CollisionPermut calling smultin_Multinomial

***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smultin_Multinomial test:
-----------------------------------------------
   N = 20,  n = 20000000,  r = 10,   t = 14,
       Sparse =   TRUE

       GenerCell = smultin_GenerCellPermut
       Number of cells = t! =        87178291200
       Expected number per cell =  1 /  4358.9146
       EColl = n^2 / (2k) =   2294.14912
       Hashing =   TRUE

       Collision test,    Mu =      2293.9736,    Sigma =    47.8841

-----------------------------------------------
Test Results for Collisions

For the total number of collisions, we use
      the Poisson approximation:
Expected number of collisions = N*Mu  :    45879.47
Observed number of collisions         :    45534
p-value of test                       :    0.95


-----------------------------
Total number of cells containing j balls

  j =  0                              :    1743165869534
  j =  1                              :        399908935
  j =  2                              :            45528
  j =  3                              :                3
  j =  4                              :                0
  j =  5                              :                0

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CPU time used                    :  00:05:00.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   d = 100000,   t =  8

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.14
p-value of test                       :    0.21

Kolmogorov-Smirnov- statistic = D-    :   0.018
p-value of test                       :    0.96

Anderson-Darling statistic = A2       :    0.82
p-value of test                       :    0.47

Test on the sum of all N observations
Number of degrees of freedom          : 3999960
Chi-square statistic                  : 4.00e+6
p-value of test                       :    0.86


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.045
p-value of test                       :    0.82

Kolmogorov-Smirnov- statistic = D-    :   0.089
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.73


-----------------------------------------------
CPU time used                    :  00:02:31.72

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 30,  n = 10000000,  r =  0,   d = 100000,   t = 16

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :   0.084
p-value of test                       :    0.62

Kolmogorov-Smirnov- statistic = D-    :   0.073
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.34
p-value of test                       :    0.91

Test on the sum of all N observations
Number of degrees of freedom          : 2999970
Chi-square statistic                  : 3.00e+6
p-value of test                       :    0.56


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.100
p-value of test                       :    0.52

Kolmogorov-Smirnov- statistic = D-    :   0.062
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.41
p-value of test                       :    0.84


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CPU time used                    :  00:02:26.15

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 24

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.13
p-value of test                       :    0.49

Kolmogorov-Smirnov- statistic = D-    :    0.18
p-value of test                       :    0.25

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.32


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :   0.075
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.15
p-value of test                       :    0.36

Anderson-Darling statistic = A2       :    0.61
p-value of test                       :    0.64


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CPU time used                    :  00:01:53.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sknuth_MaxOft test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   d = 100000,   t = 32

      Number of categories = 100000
      Expected number per category  = 100.00


-----------------------------------------------
Test results for chi2 with 99999 degrees of freedom:

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.77
p-value of test                       :    0.50

Test on the sum of all N observations
Number of degrees of freedom          : 1999980
Chi-square statistic                  : 2.00e+6
p-value of test                       :    0.73


-----------------------------------------------
Test results for Anderson-Darling:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.080
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62


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CPU time used                    :  00:02:05.46

Generator state:




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HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 40,  n = 10000000,  r =  0,   t = 8


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.054
p-value of test                       :    0.76

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.08

Anderson-Darling statistic = A2       :    1.51
p-value of test                       :    0.17

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CPU time used                    :  00:01:55.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 16


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.055
p-value of test                       :    0.85

Kolmogorov-Smirnov- statistic = D-    :    0.14
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.30
p-value of test                       :    0.94

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CPU time used                    :  00:01:18.21

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleProd test:
-----------------------------------------------
   N = 20,  n = 10000000,  r =  0,   t = 24


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.030
p-value of test                       :    0.95

Kolmogorov-Smirnov- statistic = D-    :    0.23
p-value of test                       :    0.10

Anderson-Darling statistic = A2       :    1.76
p-value of test                       :    0.13

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CPU time used                    :  00:01:36.39

Generator state:




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HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r =  0


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.77e-6
p-value of test                       :    0.9969

Kolmogorov-Smirnov- statistic = D-    : 1.97e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    1.45
p-value of test                       :    0.19

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CPU time used                    :  00:00:23.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleMean test:
-----------------------------------------------
   N = 20000000,  n = 30,  r = 10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 5.67e-5
p-value of test                       :    0.88

Kolmogorov-Smirnov- statistic = D-    : 1.96e-4
p-value of test                       :    0.21

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

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CPU time used                    :  00:00:23.94

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
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   N =  1,  n = 2000000000,  r =  0,   k = 1


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Normal statistic                      :   0.077
p-value of test                       :    0.47

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CPU time used                    :  00:00:23.73

Generator state:




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HOST = n95, Linux

AHSrandom-DT 


svaria_SampleCorr test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   k = 2


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Normal statistic                      :    0.41
p-value of test                       :    0.34

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CPU time used                    :  00:00:23.68

Generator state:




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HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 0,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.55
p-value of test                       :    0.71

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CPU time used                    :  00:01:39.31

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_AppearanceSpacings test:
-----------------------------------------------
   N =  1,   Q = 10000000,   K = 1000000000,   r = 27,   s = 3,   L = 15

   Sequences of n = (K + Q)L =  15150000000 bits
   Q = 10000000 initialization blocks
   K = 1000000000 blocks for the test
   the blocks have L = 15 bits



-----------------------------------------------
Normal statistic                      :   -0.27
p-value of test                       :    0.61

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CPU time used                    :  00:01:40.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   67.69
p-value of test                       :    0.45

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CPU time used                    :  00:00:50.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 20,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   53.70
p-value of test                       :    0.88

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CPU time used                    :  00:00:56.80

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 28,  k = 256,  Alpha =      0,  Beta =   0.25


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Number of degrees of freedom          :   67
Chi-square statistic                  :   69.86
p-value of test                       :    0.38

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CPU time used                    :  00:00:56.36

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r =  0,  k = 256,  Alpha =      0,  Beta = 0.0625


-----------------------------------------------
Number of degrees of freedom          :   37
Chi-square statistic                  :   41.81
p-value of test                       :    0.27

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CPU time used                    :  00:00:50.10

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 10,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   30.02
p-value of test                       :    0.79

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CPU time used                    :  00:00:56.44

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_WeightDistrib test:
-----------------------------------------------
   N =  1,  n = 20000000,  r = 26,  k = 256,  Alpha =      0,  Beta = 0.0625


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Number of degrees of freedom          :   37
Chi-square statistic                  :   27.63
p-value of test                       :    0.87

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CPU time used                    :  00:00:56.39

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


svaria_SumCollector test:
-----------------------------------------------
   N =  1,  n = 500000000,  r =  0,   g = 10


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Number of degrees of freedom          :   29
Chi-square statistic                  :   27.94
p-value of test                       :    0.52

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CPU time used                    :  00:01:46.68

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r =  0,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.11
p-value of test                       :    0.73

Kolmogorov-Smirnov- statistic = D-    :    0.37
p-value of test                       :    0.05

Anderson-Darling statistic = A2       :    1.49
p-value of test                       :    0.18

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   46.28
p-value of test                       :    0.23

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CPU time used                    :  00:01:03.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N = 10,  n = 1000000,  r = 25,    s = 5,    L = 30,    k = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.36

Kolmogorov-Smirnov- statistic = D-    :    0.10
p-value of test                       :    0.76

Anderson-Darling statistic = A2       :    0.38
p-value of test                       :    0.87

Test on the sum of all N observations
Number of degrees of freedom          :   40
Chi-square statistic                  :   35.67
p-value of test                       :    0.67

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CPU time used                    :  00:01:04.02

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r =  0,    s = 4,    L = 1000,    k = 1000


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Number of degrees of freedom          :    3
Chi-square statistic                  :    4.61
p-value of test                       :    0.20

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CPU time used                    :  00:01:27.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 5000,  r = 26,    s = 4,    L = 1000,    k = 1000


-----------------------------------------------
Number of degrees of freedom          :    3
Chi-square statistic                  :    0.56
p-value of test                       :    0.91

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CPU time used                    :  00:01:26.51

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r = 15,    s = 15,    L = 5000,    k = 5000


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Number of degrees of freedom          :    2
Chi-square statistic                  :    3.40
p-value of test                       :    0.18

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CPU time used                    :  00:01:16.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_MatrixRank test:
-----------------------------------------------
   N =  1,  n = 80,  r =  0,    s = 30,    L = 5000,    k = 5000


-----------------------------------------------
Number of degrees of freedom          :    2
Chi-square statistic                  :    7.13
p-value of test                       :    0.03

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CPU time used                    :  00:01:07.93

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_Savir2 test:
-----------------------------------------------
   N = 10,  n = 10000000,  r = 10,    m = 1048576,    t = 30


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.093
p-value of test                       :    0.79

Kolmogorov-Smirnov- statistic = D-    :    0.25
p-value of test                       :    0.24

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          :  130
Chi-square statistic                  :  136.19
p-value of test                       :    0.34

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CPU time used                    :  00:00:39.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


smarsa_GCD test:
-----------------------------------------------
   N = 10,  n = 50000000,  r =  0,   s = 30


-----------------------------------------------
Test results for GCD values:

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.37

Kolmogorov-Smirnov- statistic = D-    :   0.090
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    0.60
p-value of test                       :    0.64

Test on the sum of all N observations
Number of degrees of freedom          : 17430
Chi-square statistic                  :17273.40
p-value of test                       :    0.80



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CPU time used                    :  00:00:53.70

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r =  0,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   46.38
p-value of test                       :    0.12


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Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   40.59
p-value of test                       :    0.24


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Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   20.88
p-value of test                       :    0.70


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Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   24.92
p-value of test                       :    0.41


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   18.47
p-value of test                       :    0.36


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CPU time used                    :  00:00:37.18

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 25,   s = 5,   L0 =   50,   L1 =   50



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :   36
ChiSquare statistic                   :   34.96
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :   35
ChiSquare statistic                   :   36.87
p-value of test                       :    0.38


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :   25
ChiSquare statistic                   :   15.49
p-value of test                       :    0.93


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :   24
ChiSquare statistic                   :   21.81
p-value of test                       :    0.59


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Test on the values of the Statistic C

Number of degrees of freedom          :   17
ChiSquare statistic                   :   16.61
p-value of test                       :    0.48


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CPU time used                    :  00:00:37.13

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.73
p-value of test                       :    0.51


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  139.24
p-value of test                       :    0.64


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Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  497.36
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  138.64
p-value of test                       :    0.42


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   73.24
p-value of test                       :    0.50


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CPU time used                    :  00:00:44.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 20,   s = 10,   L0 = 1000,   L1 = 1000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  146
ChiSquare statistic                   :  144.68
p-value of test                       :    0.52


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  146
ChiSquare statistic                   :  147.85
p-value of test                       :    0.44


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          :  500
ChiSquare statistic                   :  532.91
p-value of test                       :    0.15


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  136
ChiSquare statistic                   :  149.86
p-value of test                       :    0.20


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Test on the values of the Statistic C

Number of degrees of freedom          :   74
ChiSquare statistic                   :   64.59
p-value of test                       :    0.77


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CPU time used                    :  00:00:43.25

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r =  0,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  336.87
p-value of test                       :    0.96


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  361.98
p-value of test                       :    0.78


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Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4814.49
p-value of test                       :    0.97


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Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  384.51
p-value of test                       :    0.40


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.22
p-value of test                       :    0.92


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CPU time used                    :  00:00:35.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


swalk_RandomWalk1 test:
-----------------------------------------------
   N =  1,  n = 1000000,  r = 15,   s = 15,   L0 = 10000,   L1 = 10000



-----------------------------------------------
Test on the values of the Statistic H

Number of degrees of freedom          :  384
ChiSquare statistic                   :  432.06
p-value of test                       :    0.05


-----------------------------------------------
Test on the values of the Statistic M

Number of degrees of freedom          :  384
ChiSquare statistic                   :  346.14
p-value of test                       :    0.92


-----------------------------------------------
Test on the values of the Statistic J

Number of degrees of freedom          : 5000
ChiSquare statistic                   : 4889.45
p-value of test                       :    0.87


-----------------------------------------------
Test on the values of the Statistic R

Number of degrees of freedom          :  378
ChiSquare statistic                   :  356.89
p-value of test                       :    0.78


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Test on the values of the Statistic C

Number of degrees of freedom          :  200
ChiSquare statistic                   :  172.36
p-value of test                       :    0.92


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CPU time used                    :  00:00:35.35

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r =  0,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    5.84
p-value of test                       :    0.92


-----------------------------------------------
Normal statistic for number of jumps  :   -0.82
p-value of test                       :    0.80



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CPU time used                    :  00:02:22.84

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LinearComp test:
-----------------------------------------------
   N =  1,  n = 400020,  r = 29,    s = 1



-----------------------------------------------
Number of degrees of freedom          :   12
Chi2 statistic for size of jumps      :    7.83
p-value of test                       :    0.80


-----------------------------------------------
Normal statistic for number of jumps  :   -0.15
p-value of test                       :    0.56



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CPU time used                    :  00:02:24.04

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r =  0,   s =   30,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.31
p-value of test                       :    0.12

Kolmogorov-Smirnov- statistic = D-    :   0.047
p-value of test                       :    0.93

Anderson-Darling statistic = A2       :    1.96
p-value of test                       :    0.10

Tests on the sum of all N observations
Standardized normal statistic         :   -1.68
p-value of test                       :    0.95

Sample variance                       :    1.03
p-value of test                       :    0.42

-----------------------------------------------
CPU time used                    :  00:01:04.28

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


scomp_LempelZiv test:
-----------------------------------------------
   N = 10,  n = 134217728,  r = 15,   s =   15,   k =   27


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.15
p-value of test                       :    0.59

Kolmogorov-Smirnov- statistic = D-    :    0.12
p-value of test                       :    0.69

Anderson-Darling statistic = A2       :    0.27
p-value of test                       :    0.96

Tests on the sum of all N observations
Standardized normal statistic         :    0.11
p-value of test                       :    0.45

Sample variance                       :    0.68
p-value of test                       :    0.73

-----------------------------------------------
CPU time used                    :  00:01:07.11

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r =  0,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    : 8.98e-3
p-value of test                       :    0.51

Kolmogorov-Smirnov- statistic = D-    : 5.98e-3
p-value of test                       :    0.74

Anderson-Darling statistic = A2       :    0.35
p-value of test                       :    0.90

-----------------------------------------------
CPU time used                    :  00:00:45.40

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sspectral_Fourier3 test:
-----------------------------------------------
   N = 100000,  n = 16384,  r = 27,   s =    3,   k =   14


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.012
p-value of test                       :    0.33

Kolmogorov-Smirnov- statistic = D-    :   0.010
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.63
p-value of test                       :    0.62

-----------------------------------------------
CPU time used                    :  00:00:44.53

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r =  0,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    5.89
p-value of test                       :    0.66

-----------------------------------------------
Global longest run of 1               :   35.00
p-value of test                       :    0.14



-----------------------------------------------
CPU time used                    :  00:01:25.23

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_LongestHeadRun test:
-----------------------------------------------
   N =  1,  n = 1000,  r = 27,   s = 3,   L = 10000020


-----------------------------------------------
Number of degrees of freedom          :    8
Chi-square statistic                  :    8.85
p-value of test                       :    0.36

-----------------------------------------------
Global longest run of 1               :   32.00
p-value of test                       :    0.50



-----------------------------------------------
CPU time used                    :  00:01:22.67

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r =  0,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.17
p-value of test                       :    0.50

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.43

Anderson-Darling statistic = A2       :    0.44
p-value of test                       :    0.80

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  192.27
p-value of test                       :    0.64

-----------------------------------------------
CPU time used                    :  00:02:04.79

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_PeriodsInStrings test:
-----------------------------------------------
   N = 10,  n = 500000000,  r = 20,   s =   10


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :   0.062
p-value of test                       :    0.89

Kolmogorov-Smirnov- statistic = D-    :    0.39
p-value of test                       :    0.04

Anderson-Darling statistic = A2       :    2.02
p-value of test                       :    0.09

Test on the sum of all N observations
Number of degrees of freedom          :  200
Chi-square statistic                  :  229.17
p-value of test                       :    0.08

-----------------------------------------------
CPU time used                    :  00:02:05.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r =  0,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.38

Kolmogorov-Smirnov- statistic = D-    :    0.17
p-value of test                       :    0.50

Anderson-Darling statistic = A2       :    0.89
p-value of test                       :    0.42

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9935.62
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:00:59.47

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingWeight2 test:
-----------------------------------------------
   N = 10,  n = 1000000000,  r = 27,   s = 3,   L = 1000000


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.29
p-value of test                       :    0.15

Kolmogorov-Smirnov- statistic = D-    :   0.091
p-value of test                       :    0.80

Anderson-Darling statistic = A2       :    1.01
p-value of test                       :    0.35

Test on the sum of all N observations
Number of degrees of freedom          : 10000
Chi-square statistic                  : 9888.93
p-value of test                       :    0.78

-----------------------------------------------
CPU time used                    :  00:01:02.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 1000000000,  r = 10,   s = 10,   L = 30



-----------------------------------------------
Normal statistic                      :   -0.49
p-value of test                       :    0.69

-----------------------------------------------
CPU time used                    :  00:01:03.95

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 300



-----------------------------------------------
Normal statistic                      :    1.07
p-value of test                       :    0.14

-----------------------------------------------
CPU time used                    :  00:01:05.88

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingCorr test:
-----------------------------------------------
   N =  1,  n = 100000000,  r = 10,   s = 10,   L = 1200



-----------------------------------------------
Normal statistic                      :  -0.052
p-value of test                       :    0.52

-----------------------------------------------
CPU time used                    :  00:04:17.37

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r =  0,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.39

Anderson-Darling statistic = A2       :    0.83
p-value of test                       :    0.46

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4875.58
p-value of test                       :    0.56

-----------------------------------------------
CPU time used                    :  00:01:52.96

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N = 10,  n = 30000000,  r = 27,   s = 3,   L = 30,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.22
p-value of test                       :    0.33

Anderson-Darling statistic = A2       :    0.69
p-value of test                       :    0.57

Test on the sum of all N observations
Number of degrees of freedom          : 4890
Chi-square statistic                  : 4849.61
p-value of test                       :    0.66

-----------------------------------------------
CPU time used                    :  00:01:53.50

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r =  0,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 3987.78
p-value of test                       :    0.92

-----------------------------------------------
CPU time used                    :  00:01:23.54

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 30000000,  r = 26,   s = 4,   L = 300,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 4117
Chi-square statistic                  : 4077.60
p-value of test                       :    0.67

-----------------------------------------------
CPU time used                    :  00:01:25.64

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r =  0,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11837.99
p-value of test                       :    0.46

-----------------------------------------------
CPU time used                    :  00:01:30.62

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_HammingIndep test:
-----------------------------------------------
   N =  1,  n = 10000000,  r = 25,   s = 5,   L = 1200,   d = 0



Counters with expected numbers >= 10
-----------------------------------------------
Number of degrees of freedom          : 11825
Chi-square statistic                  :11782.79
p-value of test                       :    0.61

-----------------------------------------------
CPU time used                    :  00:01:31.59

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r =  0,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   57.13
p-value of test                       :    0.36


-----------------------------------------------
Total number of bits:  8000125233

Normal statistic for number of bits   :    0.99
p-value of test                       :    0.16



-----------------------------------------------
CPU time used                    :  00:01:04.97

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_Run test:
-----------------------------------------------
   N =  1,  n = 2000000000,  r = 27,   s =    3


-----------------------------------------------
Total number of 1 runs:  2000000000

Number of degrees of freedom          :   54
Chi2 statistic for number of runs     :   44.79
p-value of test                       :    0.81


-----------------------------------------------
Total number of bits:  8000051712

Normal statistic for number of bits   :    0.41
p-value of test                       :    0.34



-----------------------------------------------
CPU time used                    :  00:01:05.30

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r =  0,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.21
p-value of test                       :    0.35

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.68
p-value of test                       :    0.57

Tests on the sum of all N observations
Standardized normal statistic         :    0.10
p-value of test                       :    0.46

Sample variance                       :    0.41
p-value of test                       :    0.93

-----------------------------------------------
CPU time used                    :  00:01:23.69

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r =  0,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.18
p-value of test                       :    0.47

Kolmogorov-Smirnov- statistic = D-    :    0.20
p-value of test                       :    0.40

Anderson-Darling statistic = A2       :    0.52
p-value of test                       :    0.72

Tests on the sum of all N observations
Standardized normal statistic         :    0.15
p-value of test                       :    0.44

Sample variance                       :    1.39
p-value of test                       :    0.19

-----------------------------------------------
CPU time used                    :  00:01:11.00

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000030,  r = 27,   s = 3,   d = 1


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.20
p-value of test                       :    0.39

Kolmogorov-Smirnov- statistic = D-    :    0.19
p-value of test                       :    0.42

Anderson-Darling statistic = A2       :    0.64
p-value of test                       :    0.60

Tests on the sum of all N observations
Standardized normal statistic         :   -0.36
p-value of test                       :    0.64

Sample variance                       :    0.60
p-value of test                       :    0.80

-----------------------------------------------
CPU time used                    :  00:01:24.63

Generator state:




***********************************************************
HOST = n95, Linux

AHSrandom-DT 


sstring_AutoCor test:
-----------------------------------------------
   N = 10,  n = 1000000029,  r = 27,   s = 3,   d = 3


-----------------------------------------------

Kolmogorov-Smirnov+ statistic = D+    :    0.12
p-value of test                       :    0.69

Kolmogorov-Smirnov- statistic = D-    :    0.13
p-value of test                       :    0.67

Anderson-Darling statistic = A2       :    0.24
p-value of test                       :    0.98

Tests on the sum of all N observations
Standardized normal statistic         :  -0.070
p-value of test                       :    0.53

Sample variance                       :    0.83
p-value of test                       :    0.59

-----------------------------------------------
CPU time used                    :  00:01:05.22

Generator state:





========= Summary results of BigCrush =========

 Version:          TestU01 1.2.3
 Generator:        AHSrandom-DT 
 Number of statistics:  160
 Total CPU time:   03:06:58.29

 All tests were passed




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